Activity 1 A D V A N C E D H O M E W O R K 1

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1 Activity 1 A D V A N C E D H O M E W O R K 1

2 A D V A N C E D H O M E W O R K 2 Activity 2 Research Required: Recursive Functions

3 Activity 3 A D V A N C E D H O M E W O R K 3

4 A D V A N C E D H O M E W O R K 4 Activity 4 3. Assuming that Marco continues with the pattern as it has begun, draw the next figure, size 4, and find the number of blocks in the figure. 4. Develop a mathematical model for the number of blocks in a logo of size n. 5. Compare the models that you developed for the first set of logos to the second set of logos. In what ways are they similar? In what ways are they different?

5 A D V A N C E D H O M E W O R K 5 Activity 5 How many push-ups will Scott have done after a 3. How many push-ups will Scott have done after a week? 4. Model the total number of push-ups that Scott has completed on any given day during Macho March. Include both recursive and explicit equations. 5. Will Scott meet his goal and earn the donation for the charity? Will he get a bonus? If so, how much? Explain.

6 Activity 6 A D V A N C E D H O M E W O R K 6

7 A D V A N C E D H O M E W O R K 7 Activity 7 1. If Misha uses the whole roll of fencing, what are some of the possible dimensions of the pen? 2. If Misha wants a pen with the largest possible area, what dimensions should she use for the sides? Justify your answer. 3. Write a model for the area of the rectangular pen in terms of the length of one side. Include both an equation and a graph.

8 Activity 8 A D V A N C E D H O M E W O R K 8

9 Activity 9 A D V A N C E D H O M E W O R K 9

10 Activity 10 A D V A N C E D H O M E W O R K 10

11 Activity 11 A D V A N C E D H O M E W O R K 11

12 Activity 12 A D V A N C E D H O M E W O R K 12

13 Activity 13 A D V A N C E D H O M E W O R K 13

14 A D V A N C E D H O M E W O R K 14 Activity 14 The Golden Gate Bridge is a suspension bridge spanning the Golden Gate, the opening of the San Francisco Bay into the Pacific Ocean. As part of both U.S. Route 101 and California State Route 1, the structure links the city of San Francisco, on the northern tip of the San Francisco Peninsula, to Marin Country. Golden Gate Bridge information: Two towers, which are 1,280 meters apart A suspension system that is 230 meters from the top of the tower to the surface of the water The distance between the water and the bridge is 67 meters Step #1: Make a detailed graph for The arc created by the suspension cables makes a parabola. Fix the x- axis, so that it runs along the bridge road flat surface connecting both sides. Mark the points in (x,y) form for the vertex and x-intercepts. Include the axis of symmetry. Step #2: Make a detailed graph for The arc created by the suspension cables makes a parabola. Fix the x- axis, such that the top of the two towers create a horizontal barrier. Mark the points in (x,y) form for the vertex and x-intercepts. Include the axis of symmetry. Step #3: For each of the graphs find the equation in vertex form

15 A D V A N C E D H O M E W O R K 15 Activity 15 Task: (1) Produce a one page typed report or poster with graph, images, and equations (2) Demonstrate your understanding of quadratic functions The Process: 1. Choose an arch You may select any natural or man-made arch that is of interest to you. The arch must be a permanent object with fixed dimensions that can be verified. 2. Collect data Select an image of the arch that illustrates its parabolic form. Determine the height and width of the arch, and look for information on its location and history. 3. Determine a model Use the Origin (0, 0) as one of the x-intercepts. The other x-intercept will correspond to the width of the arch. Determine the vertex using the average of the x-intercepts and the height of the arch. Write a quadratic model for your arch using all three forms of the quadratic function: Intercept Form : Vertex Form: Standard Form: 4. Summarize your results in a one page report or poster o Name of Arch and Dimensions o Image o Location o History If man-made, who designed/built it? When was it built? For what purpose? If natural, when was the arch discovered? By whom? o Algebraic Model All three forms of the Quadratic Function must be listed You need not show your work o Graph Graph of the arch showing the x-intercepts, vertex, and line of symmetry

16 A D V A N C E D H O M E W O R K 16 Challenging Quadratic Functions Problems 2

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