Determine if the function is even, odd, or neither. 1) f(x) = 8x4 + 7x + 5 A) Even B) Odd C) Neither

Size: px
Start display at page:

Download "Determine if the function is even, odd, or neither. 1) f(x) = 8x4 + 7x + 5 A) Even B) Odd C) Neither"

Transcription

1 Assignment 6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine if the function is even, odd, or neither. 1) f(x) = 8x4 + 7x + 5 1) A) Even B) Odd C) Neither The figure below shows the graph of a function y = f(x). Use this graph to solve the problem. 2) Sketch the graph of y = -f(x). 2) 1

2 Graph the point symmetric to the given point. 3) Plot (-7, 0), then plot the point that is symmetric to (-7, 0) with respect to the x-axis. 3) Determine whether the function is symmetric with respect to the y-axis, symmetric with respect to the x-axis, symmetric with respect to the origin, or none of these. 4) f(x) = (x + 5)(x + 5) 4) A) None B) x-axis only C) x-axis, y-axis, origin D) y-axis only The figure below shows the graph of a function y = f(x). Use this graph to solve the problem. 2

3 5) Sketch the graph of y = -f(x). 5) 3

4 6) Sketch the graph of y = 2f(x). 6) Determine whether the function is symmetric with respect to the y-axis, symmetric with respect to the x-axis, symmetric with respect to the origin, or none of these. 7) f(x) = 3x ) A) x-axis only B) origin only C) x-axis, y-axis, origin D) y-axis only 4

5 Graph the point symmetric to the given point. 8) Plot (9, 0), then plot the point that is symmetric to (9, 0) with respect to the origin. 8) Determine whether the function is symmetric with respect to the y-axis, symmetric with respect to the x-axis, symmetric with respect to the origin, or none of these. 9) f(x) = -8x3 + 4x 9) A) origin only B) x-axis only C) x-axis, y-axis, origin D) y-axis only Graph the function. 5

6 10) f(x) = x3-1 10) Perform the requested operation or operations. 11) f(x) = 2x + 3, g(x) = 16x ) Find (fg)(x). A) (2x + 3)(16x - 4) B) (4x - 2)( 2x + 3) C) ( 2x + 3)( 16x - 4) D) (2x + 3)(4x - 2) 6

7 12) f(x) = x + 2, g(x) = 8x ) Find (f g)(x). A) 8 x - 4 B) 8 x C) 2 2x - 1 D) 2 2x + 1 A new chocolate company is estimating how many candy bars per week college students will consume of their line of products. The graph shows the probable number of candy bars students (age 18-22) will consume from B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total number for both groups. Use the graph to answer the question. 13) Use the slopes of the line segments to decide in which period ( or ) the number 13) of candy bars per week increased more rapidly. A) B) Both increased the same C) Find the requested value. 14) Using the given tables find (f f) (10) 14) x f(x) x g(x) A) 25 B) 55 C) 10 D) 21 Consider the function h as defined. Find functions f and g so that (f g)(x) = h(x) ) h(x) = 2x ) A) f(x) = 10, g(x) = 2x + 10 B) f(x) = 10, g(x) = x C) f(x) = 2x + 10, g(x) = 10 D) f(x) = 10, g(x) = 2x + 10 x 7

8 Find the requested value. 16) The graphs of functions f and g are shown. Use these graphs to find f(-4) + g(-4). 16) y = f(x) A) -5 B) y = g(x) C) 3 D) -4 Determine whether (f g)(x) = x and whether (g f)(x) = x. 17) f(x) = 5 x - 11, g(x) = x ) A) No, yes B) No, no C) Yes, no D) Yes, yes Solve the problem. 18) The volume of water added to a circular drum of radius r is given by Vw = 35t, where Vw is 18) volume in cu ft and t is time in sec. Find the depth of water in a drum of radius 6 ft after adding water for 5 sec. (Round result to one decimal place.) A) 4.9 ft B) 3.1 ft C) 1.5 ft D) 1.2 ft Determine whether (f g)(x) = x and whether (g f)(x) = x. 19) f(x) = 1, g(x) = x 19) x A) Yes, yes B) No, no C) Yes, no D) No, yes Find the domain and range of the indicated function. 20) Find the domain and range of (fg)(x) when f(x) = 4x + 4 and g(x) = 3x ) A) Domain: 2, ; range: [0, ) B) Domain: 2, ; range: (0, ) C) Domain: - 2, ; range: (-, ) D) Domain: 2, ; range: (-, ) Given the equation or other information for a parabola, find the matching description or graph. 21) f(x) = a(x - h)2 + k, 21) a > 0; k > 0 A) The graph of f(x) intersects the x-axis twice. B) The graph of f(x) intersects the x-axis at only one point. C) You cannot tell from the information given. D) The graph of f(x) does not intersect the x-axis. 8

9 Identify the vertex of the parabola. 22) f(x) = (x + 4) ) A) (10, 0) B) (-4, 10) C) (0, -4) D) (10, -4) Find the y-intercepts and any x-intercepts. 23) y = x2 + 3x ) A) y-intercept (0, 4), x-intercept (-3, 0) B) y-intercept (0, 4), no x-intercepts C) no y-intercept, no x-intercept D) y-intercept (0, 4), x-intercept (1.33, 0) Solve the problem. 24) The table lists the amount of emissions of a certain pollutant in millions of tons. 24) Year P If the amount of emissions is modeled by a function of the form f(x) = ax2 + bx + c where x is the year, estimate the amount of emissions in the year A) 32.4 million tons B) 42.2 million tons C) 37.0 million tons D) 40.1 million tons Answer the question. 25) For what values of a does the quadratic function f(x) = ax2 + 4x + 5 have two x-intercepts? 25) A) a > 4 5 B) a > 16 5 C) a < 4 5 D) a <

10 Match the equation to the correct graph. 26) y = 2(x - 3)2-1 26) Solve the problem. 27) The height of a box is 5 inches. The length is three inches more than the width. Find the width if the 27) volume is 140 cubic inches. A) 5 in. B) 7 in. C) 4 in. D) 28 in. 10

11 Match the equation to the correct graph. 28) y = x2-5 28) Answer the question. 29) Find a quadratic function f having x-intercepts 3 and -4 and y-intercept ) A) f(x) = 2x2 + 2x - 24 B) f(x) = x2 + 5x - 24 C) f(x) = x2 + x - 24 D) f(x) = x2 + x - 12 Solve the problem. 30) A ball is tossed upward. Its height after t seconds is given in the table. 30) Time (seconds) Height (feet) Find a quadratic function to model the data. Use the model to determine when the ball reaches its maximum height, as well as the value of the maximum height. A) The ball reaches a maximum height of 40 feet in 1.5 seconds. B) The ball reaches a maximum height of 44.6 feet in 1.6 seconds. C) The ball reaches a maximum height of 50 feet in 2.1 seconds. D) The ball never reaches a maximum height. 11

Sect 4.5 Inequalities Involving Quadratic Function

Sect 4.5 Inequalities Involving Quadratic Function 71 Sect 4. Inequalities Involving Quadratic Function Objective #0: Solving Inequalities using a graph Use the graph to the right to find the following: Ex. 1 a) Find the intervals where f(x) > 0. b) Find

More information

PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to find key features. The table of values is shown below:

PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to find key features. The table of values is shown below: Math (L-3a) Learning Targets: I can find the vertex from intercept solutions calculated by quadratic formula. PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to

More information

UNIT 2: FACTOR QUADRATIC EXPRESSIONS. By the end of this unit, I will be able to:

UNIT 2: FACTOR QUADRATIC EXPRESSIONS. By the end of this unit, I will be able to: UNIT 2: FACTOR QUADRATIC EXPRESSIONS UNIT 2 By the end of this unit, I will be able to: o Represent situations using quadratic expressions in one variable o Expand and simplify quadratic expressions in

More information

7.1 Solving Quadratic Equations by Graphing

7.1 Solving Quadratic Equations by Graphing Math 2201 Date: 7.1 Solving Quadratic Equations by Graphing In Mathematics 1201, students factored difference of squares, perfect square trinomials and polynomials of the form x 2 + bx + c and ax 2 + bx

More information

Roots of Quadratic Functions

Roots of Quadratic Functions LESSON 12 Roots of Quadratic Functions LEARNING OBJECTIVES Today I am: sketching parabolas with limited information. So that I can: identify the strengths of each form of a quadratic equation. I ll know

More information

SM3 Lesson 2-3 (Intercept Form Quadratic Equation)

SM3 Lesson 2-3 (Intercept Form Quadratic Equation) SM3 Lesson 2-3 (Intercept Form Quadratic Equation) Factor the following quadratic expressions: x 2 + 11x + 30 x 2 10x 24 x 2 8x + 15 Standard Form Quadratic Equation (x + 5)(x + 6) (x 12)(x + 2) (x 5)(x

More information

VOCABULARY WORDS. quadratic equation root(s) of an equation zero(s) of a function extraneous root quadratic formula discriminant

VOCABULARY WORDS. quadratic equation root(s) of an equation zero(s) of a function extraneous root quadratic formula discriminant VOCABULARY WORDS quadratic equation root(s) of an equation zero(s) of a function extraneous root quadratic formula discriminant 1. Each water fountain jet creates a parabolic stream of water. You can represent

More information

2. To receive credit on any problem, you must show work that explains how you obtained your answer or you must explain how you obtained your answer.

2. To receive credit on any problem, you must show work that explains how you obtained your answer or you must explain how you obtained your answer. Math 50, Spring 2006 Test 2 PRINT your name on the back of the test. Circle your class: MW @ 11 TTh @ 2:30 Directions 1. Time limit: 50 minutes. 2. To receive credit on any problem, you must show work

More information

y-intercept remains constant?

y-intercept remains constant? 1. The graph of a line that contains the points ( 1, 5) and (4, 5) is shown below. Which best represents this line if the slope is doubled and the y-intercept remains constant? F) G) H) J) 2. The graph

More information

Length of a Side (m)

Length of a Side (m) Quadratics Day 1 The graph shows length and area data for rectangles with a fixed perimeter. Area (m ) 450 400 350 300 50 00 150 100 50 5 10 15 0 5 30 35 40 Length of a Side (m) 1. Describe the shape of

More information

Student Exploration: Quadratics in Factored Form

Student Exploration: Quadratics in Factored Form Name: Date: Student Exploration: Quadratics in Factored Form Vocabulary: factored form of a quadratic function, linear factor, parabola, polynomial, quadratic function, root of an equation, vertex of a

More information

Honors Algebra 2 Assignment Sheet - Chapter 1

Honors Algebra 2 Assignment Sheet - Chapter 1 Assignment Sheet - Chapter 1 #01: Read the text and the examples in your book for the following sections: 1.1, 1., and 1.4. Be sure you read and understand the handshake problem. Also make sure you copy

More information

For Questions 1-15, NO CALCULATOR!

For Questions 1-15, NO CALCULATOR! For Questions 1-15, NO CALCULATOR! 1. Identify the y-intercept: Identify the vertex: 2. The revenue, R(x), generated by an increase in price of x dollars for an item is represented by the equation Identify

More information

Determine the intercepts of the line and ellipse below: Definition: An intercept is a point of a graph on an axis. Line: x intercept(s)

Determine the intercepts of the line and ellipse below: Definition: An intercept is a point of a graph on an axis. Line: x intercept(s) Topic 1 1 Intercepts and Lines Definition: An intercept is a point of a graph on an axis. For an equation Involving ordered pairs (x, y): x intercepts (a, 0) y intercepts (0, b) where a and b are real

More information

Algebra II B Review 3

Algebra II B Review 3 Algebra II B Review 3 Multiple Choice Identify the choice that best completes the statement or answers the question. Graph the equation. Describe the graph and its lines of symmetry. 1. a. c. b. graph

More information

Up and Down or Down and Up

Up and Down or Down and Up Lesson.1 Assignment Name Date Up and Down or Down and Up Exploring Quadratic Functions 1. The citizens of Herrington County are wild about their dogs. They have an existing dog park for dogs to play, but

More information

Math 138 Exam 1 Review Problems Fall 2008

Math 138 Exam 1 Review Problems Fall 2008 Chapter 1 NOTE: Be sure to review Activity Set 1.3 from the Activity Book, pp 15-17. 1. Sketch an algebra-piece model for the following problem. Then explain or show how you used it to arrive at your solution.

More information

Sect Linear Equations in Two Variables

Sect Linear Equations in Two Variables 99 Concept # Sect. - Linear Equations in Two Variables Solutions to Linear Equations in Two Variables In this chapter, we will examine linear equations involving two variables. Such equations have an infinite

More information

Hyperbolas Graphs, Equations, and Key Characteristics of Hyperbolas Forms of Hyperbolas p. 583

Hyperbolas Graphs, Equations, and Key Characteristics of Hyperbolas Forms of Hyperbolas p. 583 C H A P T ER Hyperbolas Flashlights concentrate beams of light by bouncing the rays from a light source off a reflector. The cross-section of a reflector can be described as hyperbola with the light source

More information

Math Exam 1 Review Fall 2009

Math Exam 1 Review Fall 2009 Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice some kinds of problems. This collection is not necessarily exhaustive.

More information

This early Greek study was largely concerned with the geometric properties of conics.

This early Greek study was largely concerned with the geometric properties of conics. 4.3. Conics Objectives Recognize the four basic conics: circle, ellipse, parabola, and hyperbola. Recognize, graph, and write equations of parabolas (vertex at origin). Recognize, graph, and write equations

More information

ore C ommon Core Edition APlgebra Algebra 1 ESTS RACTICE PRACTICE TESTS Topical Review Book Company Topical Review Book Company

ore C ommon Core Edition APlgebra Algebra 1 ESTS RACTICE PRACTICE TESTS Topical Review Book Company Topical Review Book Company C ommon Core ommon Edition C ore Edition Algebra 1 APlgebra 1 T RACTICE ESTS Answer Keys PRACTICE TESTS Topical Review Book Company Topical Review Book Company TEST 1 Part I 1. 3 5. 2 9. 4 13. 1 17. 4

More information

E. Slope-Intercept Form and Direct Variation (pp )

E. Slope-Intercept Form and Direct Variation (pp ) and Direct Variation (pp. 32 35) For any two points, there is one and only one line that contains both points. This fact can help you graph a linear equation. Many times, it will be convenient to use the

More information

Block: Date: Name: REVIEW Linear Equations. 7.What is the equation of the line that passes through the point (5, -3) and has a slope of -3?

Block: Date: Name: REVIEW Linear Equations. 7.What is the equation of the line that passes through the point (5, -3) and has a slope of -3? Name: REVIEW Linear Equations 1. What is the slope of the line y = -2x + 3? 2. Write the equation in slope-intercept form. Block: Date: 7.What is the equation of the line that passes through the point

More information

In this section, we find equations for straight lines lying in a coordinate plane.

In this section, we find equations for straight lines lying in a coordinate plane. 2.4 Lines Lines In this section, we find equations for straight lines lying in a coordinate plane. The equations will depend on how the line is inclined. So, we begin by discussing the concept of slope.

More information

Activity Overview This activity takes the concept of derivative and applies it to various maximum and minimum problems.

Activity Overview This activity takes the concept of derivative and applies it to various maximum and minimum problems. TI-Nspire Activity: Derivatives: Applied Maxima and Minima By: Tony Duncan Activity Overview This activity takes the concept of derivative and applies it to various maximum and minimum problems. Concepts

More information

SECONDARY 2H ~ UNIT 5 (Intro to Quadratics)

SECONDARY 2H ~ UNIT 5 (Intro to Quadratics) SECONDARY 2H ~ UNIT 5 (Intro to Quadratics) Assignments from your Student Workbook are labeled WB Those from your hardbound Student Resource Book are labeled RB. Do all work from the Student Resource Book

More information

Chapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane

Chapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Chapter 9 Linear equations/graphing 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Rectangular Coordinate System Quadrant II (-,+) y-axis Quadrant

More information

The Picture Tells the Linear Story

The Picture Tells the Linear Story The Picture Tells the Linear Story Students investigate the relationship between constants and coefficients in a linear equation and the resulting slopes and y-intercepts on the graphs. This activity also

More information

Slope-Intercept Form. Find the x- and y-intercepts. 1. y 3x 6 2. y 2x 8. Graph each equation. 3. y 1 x 3 4. y 5x 5 5. y x 4

Slope-Intercept Form. Find the x- and y-intercepts. 1. y 3x 6 2. y 2x 8. Graph each equation. 3. y 1 x 3 4. y 5x 5 5. y x 4 Practice A Slope-Intercept Form Find the x- and y-intercepts. 1. y 3x 6. y x 8 _ Graph each equation. 3. y 1 x 3 4. y 5x 5 5. y x 4 Write the equation of the line in slope-intercept form. 6. 7. _ Practice

More information

Year 11 Graphing Notes

Year 11 Graphing Notes Year 11 Graphing Notes Terminology It is very important that students understand, and always use, the correct terms. Indeed, not understanding or using the correct terms is one of the main reasons students

More information

Graphing Sine and Cosine

Graphing Sine and Cosine The problem with average monthly temperatures on the preview worksheet is an example of a periodic function. Periodic functions are defined on p.254 Periodic functions repeat themselves each period. The

More information

Pre-AP Algebra 2 Unit 8 - Lesson 2 Graphing rational functions by plugging in numbers; feature analysis

Pre-AP Algebra 2 Unit 8 - Lesson 2 Graphing rational functions by plugging in numbers; feature analysis Pre-AP Algebra 2 Unit 8 - Lesson 2 Graphing rational functions by plugging in numbers; feature analysis Objectives: Students will be able to: Analyze the features of a rational function: determine domain,

More information

Arkansas Council of Teachers of Mathematics Regional Algebra I Contest March 3, 2012

Arkansas Council of Teachers of Mathematics Regional Algebra I Contest March 3, 2012 Arkansas Council of Teachers of Mathematics Regional Algebra I Contest March 3, 2012 For questions 1 through 25, mark your answer choice on the answer sheet provided. Make sure that any erasures are cleanly

More information

PREREQUISITE/PRE-CALCULUS REVIEW

PREREQUISITE/PRE-CALCULUS REVIEW PREREQUISITE/PRE-CALCULUS REVIEW Introduction This review sheet is a summary of most of the main topics that you should already be familiar with from your pre-calculus and trigonometry course(s), and which

More information

You analyzed graphs of functions. (Lesson 1-5)

You analyzed graphs of functions. (Lesson 1-5) You analyzed graphs of functions. (Lesson 1-5) LEQ: How do we graph transformations of the sine and cosine functions & use sinusoidal functions to solve problems? sinusoid amplitude frequency phase shift

More information

Use smooth curves to complete the graph between and beyond the vertical asymptotes.

Use smooth curves to complete the graph between and beyond the vertical asymptotes. 5.3 Graphs of Rational Functions Guidelines for Graphing Rational Functions 1. Find and plot the x-intercepts. (Set numerator = 0 and solve for x) 2. Find and plot the y-intercepts. (Let x = 0 and solve

More information

SECONDARY 2H ~ UNIT 5 (Into to Quadratics)

SECONDARY 2H ~ UNIT 5 (Into to Quadratics) SECONDARY 2H ~ UNIT 5 (Into to Quadratics) Assignments from your Student Workbook are labeled WB Those from your hardbound Student Resource Book are labeled RB. Do all work from the Student Resource Book

More information

Review for Mastery. Identifying Linear Functions

Review for Mastery. Identifying Linear Functions Identifying Linear Functions You can determine if a function is linear by its graph, ordered pairs, or equation. Identify whether the graph represents a linear function. Step 1: Determine whether the graph

More information

Section 5.2 Graphs of the Sine and Cosine Functions

Section 5.2 Graphs of the Sine and Cosine Functions A Periodic Function and Its Period Section 5.2 Graphs of the Sine and Cosine Functions A nonconstant function f is said to be periodic if there is a number p > 0 such that f(x + p) = f(x) for all x in

More information

THE DOMAIN AND RANGE OF A FUNCTION Basically, all functions do is convert inputs into outputs.

THE DOMAIN AND RANGE OF A FUNCTION Basically, all functions do is convert inputs into outputs. THE DOMAIN AND RANGE OF A FUNCTION Basically, all functions do is convert inputs into outputs. Exercise #1: Consider the function y = f (x) shown on the graph below. (a) Evaluate each of the following:

More information

ANNOUNCEMENTS. GOOD MORNING or GOOD AFTERNOON AGENDA FOR TODAY. Quickly Review Absolute Values Graphing Quadratics. Vertex Form Calculator Activity

ANNOUNCEMENTS. GOOD MORNING or GOOD AFTERNOON AGENDA FOR TODAY. Quickly Review Absolute Values Graphing Quadratics. Vertex Form Calculator Activity ANNOUNCEMENTS GOOD MORNING or GOOD AFTERNOON AGENDA FOR TODAY Quickly Review Absolute Values Graphing Quadratics Vertex Form Calculator Activity M314 Algebra II Section 9-4 and 9-5: Quadratics Presented

More information

Actual testimonials from people that have used the survival guide:

Actual testimonials from people that have used the survival guide: Algebra 1A Unit: Coordinate Plane Assignment Sheet Name: Period: # 1.) Page 206 #1 6 2.) Page 206 #10 26 all 3.) Worksheet (SIF/Standard) 4.) Worksheet (SIF/Standard) 5.) Worksheet (SIF/Standard) 6.) Worksheet

More information

Accuplacer Math Packet

Accuplacer Math Packet College Level Math Accuplacer Math Packet 1. 23 0 2. 5 8 5-6 a. 0 b. 23 c. 1 d. None of the above. a. 5-48 b. 5 48 c. 5 14 d. 5 2 3. (6x -3 y 5 )(-7x 2 y -9 ) a. 42x -6 y -45 b. -42x -6 y -45 c. -42x -1

More information

Practice Test 3 (longer than the actual test will be) 1. Solve the following inequalities. Give solutions in interval notation. (Expect 1 or 2.

Practice Test 3 (longer than the actual test will be) 1. Solve the following inequalities. Give solutions in interval notation. (Expect 1 or 2. MAT 115 Spring 2015 Practice Test 3 (longer than the actual test will be) Part I: No Calculators. Show work. 1. Solve the following inequalities. Give solutions in interval notation. (Expect 1 or 2.) a.

More information

4.4 Slope and Graphs of Linear Equations. Copyright Cengage Learning. All rights reserved.

4.4 Slope and Graphs of Linear Equations. Copyright Cengage Learning. All rights reserved. 4.4 Slope and Graphs of Linear Equations Copyright Cengage Learning. All rights reserved. 1 What You Will Learn Determine the slope of a line through two points Write linear equations in slope-intercept

More information

Scatter Plots, Correlation, and Lines of Best Fit

Scatter Plots, Correlation, and Lines of Best Fit Lesson 7.3 Objectives Interpret a scatter plot. Identify the correlation of data from a scatter plot. Find the line of best fit for a set of data. Scatter Plots, Correlation, and Lines of Best Fit A video

More information

The Sine Function. Precalculus: Graphs of Sine and Cosine

The Sine Function. Precalculus: Graphs of Sine and Cosine Concepts: Graphs of Sine, Cosine, Sinusoids, Terminology (amplitude, period, phase shift, frequency). The Sine Function Domain: x R Range: y [ 1, 1] Continuity: continuous for all x Increasing-decreasing

More information

Study Guide and Review - Chapter 3. Find the x-intercept and y-intercept of the graph of each linear function.

Study Guide and Review - Chapter 3. Find the x-intercept and y-intercept of the graph of each linear function. Find the x-intercept and y-intercept of the graph of each linear function. 11. The x-intercept is the point at which the y-coordinate is 0, or the line crosses the x-axis. So, the x-intercept is 8. The

More information

5.1 Graphing Sine and Cosine Functions.notebook. Chapter 5: Trigonometric Functions and Graphs

5.1 Graphing Sine and Cosine Functions.notebook. Chapter 5: Trigonometric Functions and Graphs Chapter 5: Trigonometric Functions and Graphs 1 Chapter 5 5.1 Graphing Sine and Cosine Functions Pages 222 237 Complete the following table using your calculator. Round answers to the nearest tenth. 2

More information

Section 6.3: Factored Form of a Quadratic Function

Section 6.3: Factored Form of a Quadratic Function Section 6.3: Factored Form of a Quadratic Function make the connection between the factored form of a quadratic and the x-intercepts of the graph Forms of a Quadratic Function (i) Standard Form (ii) Factored

More information

Chapter 8. Lesson a. (2x+3)(x+2) b. (2x+1)(3x+2) c. no solution d. (2x+y)(y+3) ; Conclusion. Not every expression can be factored.

Chapter 8. Lesson a. (2x+3)(x+2) b. (2x+1)(3x+2) c. no solution d. (2x+y)(y+3) ; Conclusion. Not every expression can be factored. Chapter 8 Lesson 8.1.1 8-1. a. (x+4)(y+x+) = xy+x +6x+4y+8 b. 18x +9x 8-. a. (x+3)(x+) b. (x+1)(3x+) c. no solution d. (x+y)(y+3) ; Conclusion. Not every expression can be factored. 8-3. a. (3x+1)(x+5)=6x

More information

Unit 8 Trigonometry. Math III Mrs. Valentine

Unit 8 Trigonometry. Math III Mrs. Valentine Unit 8 Trigonometry Math III Mrs. Valentine 8A.1 Angles and Periodic Data * Identifying Cycles and Periods * A periodic function is a function that repeats a pattern of y- values (outputs) at regular intervals.

More information

MTH 1825 Sample Exam 4 Fall 2014

MTH 1825 Sample Exam 4 Fall 2014 Name (print) Section Signature PID Instructions: Please check to make sure your exam has all 8 pages (including cover) before you begin. Please read the following instructions carefully. 1. DO NOT OPEN

More information

Ch. 6 Linear Functions Notes

Ch. 6 Linear Functions Notes First Name: Last Name: Block: Ch. 6 Linear Functions Notes 6.1 SLOPE OF A LINE Ch. 6.1 HW: p. 9 #4 1, 17,,, 8 6. SLOPES OF PARALLEL AND PERPENDICULAR LINES 6 Ch. 6. HW: p. 49 # 6 odd letters, 7 0 8 6.

More information

Logarithmic Functions

Logarithmic Functions C H A P T ER Logarithmic Functions The human ear is capable of hearing sounds across a wide dynamic range. The softest noise the average human can hear is 0 decibels (db), which is equivalent to a mosquito

More information

2.3 Quick Graphs of Linear Equations

2.3 Quick Graphs of Linear Equations 2.3 Quick Graphs of Linear Equations Algebra III Mr. Niedert Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 1 / 11 Forms of a Line Slope-Intercept Form The slope-intercept form of a linear

More information

MATH Exam 2 Solutions November 16, 2015

MATH Exam 2 Solutions November 16, 2015 MATH 1.54 Exam Solutions November 16, 15 1. Suppose f(x, y) is a differentiable function such that it and its derivatives take on the following values: (x, y) f(x, y) f x (x, y) f y (x, y) f xx (x, y)

More information

6.1.2: Graphing Quadratic Equations

6.1.2: Graphing Quadratic Equations 6.1.: Graphing Quadratic Equations 1. Obtain a pair of equations from your teacher.. Press the Zoom button and press 6 (for ZStandard) to set the window to make the max and min on both axes go from 10

More information

5.3 Trigonometric Graphs. Copyright Cengage Learning. All rights reserved.

5.3 Trigonometric Graphs. Copyright Cengage Learning. All rights reserved. 5.3 Trigonometric Graphs Copyright Cengage Learning. All rights reserved. Objectives Graphs of Sine and Cosine Graphs of Transformations of Sine and Cosine Using Graphing Devices to Graph Trigonometric

More information

Chapter 4 Trigonometric Functions

Chapter 4 Trigonometric Functions Chapter 4 Trigonometric Functions Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Radian and Degree Measure Trigonometric Functions: The Unit Circle Right Triangle Trigonometry

More information

Optimization Exploration: The Inscribed Rectangle. Learning Objectives: Materials:

Optimization Exploration: The Inscribed Rectangle. Learning Objectives: Materials: Optimization Exploration: The Inscribed Rectangle Lesson Information Written by Jonathan Schweig and Shira Sand Subject: Pre-Calculus Calculus Algebra Topic: Functions Overview: Students will explore some

More information

constant EXAMPLE #4:

constant EXAMPLE #4: Linear Equations in One Variable (1.1) Adding in an equation (Objective #1) An equation is a statement involving an equal sign or an expression that is equal to another expression. Add a constant value

More information

Lesson 6.1 Linear Equation Review

Lesson 6.1 Linear Equation Review Name: Lesson 6.1 Linear Equation Review Vocabulary Equation: a math sentence that contains Linear: makes a straight line (no Variables: quantities represented by (often x and y) Function: equations can

More information

Skills Practice Skills Practice for Lesson 4.1

Skills Practice Skills Practice for Lesson 4.1 Skills Practice Skills Practice for Lesson.1 Name Date Squares and More Using Patterns to Generate Algebraic Functions Vocabulary Match each word with its corresponding definition. 1. linear function a.

More information

2.3: The Human Cannonball

2.3: The Human Cannonball 2.3: The Human Cannonball Parabola Equations and Graphs As a human cannonball Rosa is shot from a special cannon. She is launched into the air by a spring. Rosa lands in a horizontal net 150 ft. from the

More information

Intermediate Mathematics League of Eastern Massachusetts

Intermediate Mathematics League of Eastern Massachusetts Meet #5 April 2003 Intermediate Mathematics League of Eastern Massachusetts www.imlem.org Meet #5 April 2003 Category 1 Mystery You may use a calculator 1. In his book In an Average Lifetime, author Tom

More information

Section 7.2 Logarithmic Functions

Section 7.2 Logarithmic Functions Math 150 c Lynch 1 of 6 Section 7.2 Logarithmic Functions Definition. Let a be any positive number not equal to 1. The logarithm of x to the base a is y if and only if a y = x. The number y is denoted

More information

M.I. Transformations of Functions

M.I. Transformations of Functions M.I. Transformations of Functions Do Now: A parabola with equation y = (x 3) 2 + 8 is translated. The image of the parabola after the translation has an equation of y = (x + 5) 2 4. Describe the movement.

More information

Products of Linear Functions

Products of Linear Functions Math Objectives Students will understand relationships between the horizontal intercepts of two linear functions and the horizontal intercepts of the quadratic function resulting from their product. Students

More information

The Geometric Definitions for Circles and Ellipses

The Geometric Definitions for Circles and Ellipses 18 Conic Sections Concepts: The Origin of Conic Sections Equations and Graphs of Circles and Ellipses The Geometric Definitions for Circles and Ellipses (Sections 10.1-10.3) A conic section or conic is

More information

Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. y = 4x + 3

Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. y = 4x + 3 Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. y = 4x + 3 Rewrite the equation in standard form. The equation is now in standard form

More information

Discussion 8 Solution Thursday, February 10th. Consider the function f(x, y) := y 2 x 2.

Discussion 8 Solution Thursday, February 10th. Consider the function f(x, y) := y 2 x 2. Discussion 8 Solution Thursday, February 10th. 1. Consider the function f(x, y) := y 2 x 2. (a) This function is a mapping from R n to R m. Determine the values of n and m. The value of n is 2 corresponding

More information

Pre Calc. Conics.

Pre Calc. Conics. 1 Pre Calc Conics 2015 03 24 www.njctl.org 2 Table of Contents click on the topic to go to that section Review of Midpoint and Distance Formulas Intro to Conic Sections Parabolas Circles Ellipses Hyperbolas

More information

June 2016 Regents GEOMETRY COMMON CORE

June 2016 Regents GEOMETRY COMMON CORE 1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation? 4) 2

More information

2.3 BUILDING THE PERFECT SQUARE

2.3 BUILDING THE PERFECT SQUARE 16 2.3 BUILDING THE PERFECT SQUARE A Develop Understanding Task Quadratic)Quilts Optimahasaquiltshopwhereshesellsmanycolorfulquiltblocksforpeoplewhowant tomaketheirownquilts.shehasquiltdesignsthataremadesothattheycanbesized

More information

Algebra EOC Practice Test #3

Algebra EOC Practice Test #3 Class: Date: Algebra EOC Practice Test #3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the monomial 4x 2 y 3y 3 without the use of negative exponents.

More information

MATH Review Exam II 03/06/11

MATH Review Exam II 03/06/11 MATH 21-259 Review Exam II 03/06/11 1. Find f(t) given that f (t) = sin t i + 3t 2 j and f(0) = i k. 2. Find lim t 0 3(t 2 1) i + cos t j + t t k. 3. Find the points on the curve r(t) at which r(t) and

More information

Chapter 4. Lesson Lesson The parabola should pass through the points (0, 0) and (2, 0) and have vertex (1, 1).

Chapter 4. Lesson Lesson The parabola should pass through the points (0, 0) and (2, 0) and have vertex (1, 1). Chapter 4 Lesson 4.1.1 4-3. The parabola should pass through the points (0, 0) and (2, 0) and have vertex (1, 1). 4-4. She should have received two sports cars and ten pieces of furniture. 4-5. 1 3 ( 2x)=

More information

Name: Date: Period: Activity 4.6.2: Point-Slope Form of an Equation. 0, 4 and moving to another point on the line using the slope.

Name: Date: Period: Activity 4.6.2: Point-Slope Form of an Equation. 0, 4 and moving to another point on the line using the slope. Name: Date: Period: Activity.6.2: Point-Slope Form of an Equation 1.) Graph the equation y x = + starting at ( ) 0, and moving to another point on the line using the slope. 2.) Now, draw another graph

More information

14.2 Limits and Continuity

14.2 Limits and Continuity 14 Partial Derivatives 14.2 Copyright Cengage Learning. All rights reserved. Copyright Cengage Learning. All rights reserved. Let s compare the behavior of the functions Tables 1 2 show values of f(x,

More information

Now we are going to introduce a new horizontal axis that we will call y, so that we have a 3-dimensional coordinate system (x, y, z).

Now we are going to introduce a new horizontal axis that we will call y, so that we have a 3-dimensional coordinate system (x, y, z). Example 1. A circular cone At the right is the graph of the function z = g(x) = 16 x (0 x ) Put a scale on the axes. Calculate g(2) and illustrate this on the diagram: g(2) = 8 Now we are going to introduce

More information

3 Kevin s work for deriving the equation of a circle is shown below.

3 Kevin s work for deriving the equation of a circle is shown below. June 2016 1. A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation?

More information

You identified, analyzed, and graphed quadratic functions. (Lesson 1 5) Analyze and graph equations of parabolas. Write equations of parabolas.

You identified, analyzed, and graphed quadratic functions. (Lesson 1 5) Analyze and graph equations of parabolas. Write equations of parabolas. You identified, analyzed, and graphed quadratic functions. (Lesson 1 5) Analyze and graph equations of parabolas. Write equations of parabolas. conic section degenerate conic locus parabola focus directrix

More information

Directions: Show all of your work. Use units and labels and remember to give complete answers.

Directions: Show all of your work. Use units and labels and remember to give complete answers. AMS II QTR 4 FINAL EXAM REVIEW TRIANGLES/PROBABILITY/UNIT CIRCLE/POLYNOMIALS NAME HOUR This packet will be collected on the day of your final exam. Seniors will turn it in on Friday June 1 st and Juniors

More information

Pre-Calc Conics

Pre-Calc Conics Slide 1 / 160 Slide 2 / 160 Pre-Calc Conics 2015-03-24 www.njctl.org Slide 3 / 160 Table of Contents click on the topic to go to that section Review of Midpoint and Distance Formulas Intro to Conic Sections

More information

coordinate system: (0, 2), (0, 0), (0, 3).

coordinate system: (0, 2), (0, 0), (0, 3). Lesson. Objectives Find the slope of a line from the graph of the line. Find the slope of a line given two points on the line. Activity The Slope of a Line A surveyor places two stakes, A and B, on the

More information

9/11/2017 Assignment Previewer

9/11/2017 Assignment Previewer 41 Multivariable Functions I (10998039) Due: Wed Sep 13 2017 03:00 PM MDT Question 1 2 3 4 5 6 7 8 9 10 11 Instructions Notes and Learning Goals Flash Graphing App 1. Question Details SCalcET8 14.1.007.

More information

Math 165 Section 3.1 Linear Functions

Math 165 Section 3.1 Linear Functions Math 165 Section 3.1 Linear Functions - complete this page Read the book or the power point presentations for this section. Complete all questions on this page Also complete all questions on page 6 1)

More information

Conic and Quadric Surface Lab page 4. NORTHEASTERN UNIVERSITY Department of Mathematics Fall 03 Conic Sections and Quadratic Surface Lab

Conic and Quadric Surface Lab page 4. NORTHEASTERN UNIVERSITY Department of Mathematics Fall 03 Conic Sections and Quadratic Surface Lab Conic and Quadric Surface Lab page 4 NORTHEASTERN UNIVERSITY Department of Mathematics Fall 03 Conic Sections and Quadratic Surface Lab Goals By the end of this lab you should: 1.) Be familar with the

More information

Algebra & Trig. 1. , then the slope of the line is given by

Algebra & Trig. 1. , then the slope of the line is given by Algebra & Trig. 1 1.4 and 1.5 Linear Functions and Slope Slope is a measure of the steepness of a line and is denoted by the letter m. If a nonvertical line passes through two distinct points x, y 1 1

More information

Pre-Calc. Slide 1 / 160. Slide 2 / 160. Slide 3 / 160. Conics Table of Contents. Review of Midpoint and Distance Formulas

Pre-Calc. Slide 1 / 160. Slide 2 / 160. Slide 3 / 160. Conics Table of Contents. Review of Midpoint and Distance Formulas Slide 1 / 160 Pre-Calc Slide 2 / 160 Conics 2015-03-24 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 160 Review of Midpoint and Distance Formulas Intro to Conic Sections

More information

Answers for the lesson Plot Points in a Coordinate Plane

Answers for the lesson Plot Points in a Coordinate Plane LESSON 3.1 Answers for the lesson Plot Points in a Coordinate Plane Skill Practice 1. 5; 23 2. No; the point could lie in either Quadrant II or Quadrant IV. 3. (3, 22) 4. (, 21) 5. (4, 4) 6. (24, 3) 7.

More information

Chapter 9. Conic Sections and Analytic Geometry. 9.1 The Ellipse. Copyright 2014, 2010, 2007 Pearson Education, Inc.

Chapter 9. Conic Sections and Analytic Geometry. 9.1 The Ellipse. Copyright 2014, 2010, 2007 Pearson Education, Inc. Chapter 9 Conic Sections and Analytic Geometry 9.1 The Ellipse Copyright 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Graph ellipses centered at the origin. Write equations of ellipses in standard

More information

8.5 Training Day Part II

8.5 Training Day Part II 26 8.5 Training Day Part II A Solidify Understanding Task Fernando and Mariah continued training in preparation for the half marathon. For the remaining weeks of training, they each separately kept track

More information

Copyright 2009 Pearson Education, Inc. Slide Section 8.2 and 8.3-1

Copyright 2009 Pearson Education, Inc. Slide Section 8.2 and 8.3-1 8.3-1 Transformation of sine and cosine functions Sections 8.2 and 8.3 Revisit: Page 142; chapter 4 Section 8.2 and 8.3 Graphs of Transformed Sine and Cosine Functions Graph transformations of y = sin

More information

Practice problems from old exams for math 233

Practice problems from old exams for math 233 Practice problems from old exams for math 233 William H. Meeks III January 14, 2010 Disclaimer: Your instructor covers far more materials that we can possibly fit into a four/five questions exams. These

More information

Warm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011.

Warm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. Warm-Up Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. You have 20 minutes at the beginning of class to work on these three tasks.

More information

Lab 4 Projectile Motion

Lab 4 Projectile Motion b Lab 4 Projectile Motion What You Need To Know: x x v v v o ox ox v v ox at 1 t at a x FIGURE 1 Linear Motion Equations The Physics So far in lab you ve dealt with an object moving horizontally or an

More information

Part 5: Math. Chapter 28: Numbers, Arithmetic, and Number Sense ( ) +? Questions. Bonus Chapter

Part 5: Math. Chapter 28: Numbers, Arithmetic, and Number Sense ( ) +? Questions. Bonus Chapter Bonus Chapter Chapter 28: Numbers, Arithmetic, and Number Sense Questions 1. The speed of light is about 186,000 miles per second. A light year is the distance light travels in a year. What is the approximate

More information