Name: Algebra 1: Intro to Quadratic Functions and Graphing Part 1

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1 Hour: Name: Algebra 1: Intro to Quadratic Functions and Graphing Part 1 Use the link below for the Quadratic Explorer to investigate graphs of quadratic functions. Fill in the blanks using the function y = ax 2 + bx + c. com/quadraticexplorenhtml The maximum or minimum is called the b c IPA The line of reflection is called the verh e The y-intercept is (0, ). The y-intercept is not affected by 1i or The x-coordinate of the vertex is affected by and b, but not by The graph opens up if a If the graph opens up, then there is a If the graph opens down, then there is a r 6IA and the graph opens down if e As the absolute value of "a" gets larger, the graph becomes As the absolute value of "a" gets smaller, the graph becomes To find the equation for the take the average of the x-coordinates of two x-intercepts (or any two points with the same y-coordinate). If you substitute this x coordinate into the original equation, you will find the y coordinate of the

2 Example: Use the function y =x 2 2x 3 to answer the questions and fill in the blanks. Then graph the function by creating a table of values. Does the graph have a maximum or minimum? n Is the graph wider or narrower than the graph of y = 4x2 5? C. ro - What is the y-intercept? What is the equation of the axis of symmetry? ) What are the coordinates of the vertex? (A A x2-2x-3 y '. 1 -/ a?t 0 I i 1 3; :1) 2 (a, 3 Example: Use the function y = 2x2 +18 to answer the questions and fill in the blanks. Then graph the function by creating a table of values. 011),11/ ) Does the graph have a maximum or minimum? Is the graph wider or narrower than the graph of y = 0.25x2 3x +8? //1 What is the y-intercept? (,, What is the equation of the axis of symmetry?, What are the coordinates of the vertex? 2 i ' t A 1 2 ) ',, 3 I I, Id

3 Hour: Name: Algebra 1: Intro to Quadratic Functions and Graphing Worksheet 1 1. Use the function y = x2 x 2 to answer the questions and fill in the blanks. Then graph the function by creating a table of values. x up Does the graph have a maximum or minimum? n Is the graph wider or narrower than the graph of y = 3x2 2x + 5? Wider What is the y-intercept? ) 2) What is the equation of the axis of symmetry? X = a(t) 1 What are the coordinates a the vertex? ( 2) 2_ 2- - (-1) A V ) 23- I 2 (- 2) 1-- (-- 2) 2, = LI" + -I (-1)' - (-0 - = I -t- I - 0 o i 2-- / _ _ 2 i -=. ii- 2 2_ 0 2. Use the function y = x2 + x + 6 to answer the questions and fill in the blanks. Then graph the function by creating a table of values. do vivi Does the graph have a maximum or minimum? Is the graph wider or narrower than the graph of y = 0.5x2 + 5x? rorro We r What is the y-intercept? (0 ) 0 I I What is the equation of the axis of symmetry? r 'QC-0 2_ What are the coordinates of the vertex? V, 0,5 b +x ) , i, I 4 2 (-- 2-4"--/It4-4 = +4, 0-1 -(-1)2-14-6= if Co 1 2 -as -1-2 V

4 1 Use the function y = 2x - 6x + 4 to answer the questions and fill in the blanks. Then graph the function by creating a table of values. (Ap Does the graph have a maximum or minimum? Mit) Is the graph wider or narrower than the graph of y = x2 + 3? narrow What is the y-intercept? ) What is the equation of the axis of symmetry? P": AU) t What are the coordinates of the vertex? 2 Z 3/2 VA) Li- = 4-5 x *2)2-6,(-2.) 4- LI- = (5,4-1 z 4- V- 11/ -1 9-(-1)'-6(--044 = t2-1 2 (1) 2.- 6(i)4I-7 0? -6 4-(4 0 2 t-/ M = IIMIIIIIIIHIN WIN = = MNIMIMI MIIIM WW ThIIIIMEN =Mr E = / MINIMUM = M MENU= KIN IIIIIM MENNEN= 1= M = M Axis of )11"11' 1 4. Use the function y = -x 2 -x-4 to answer the questions and fill in the blanks. 2 Then graph the function by creating a table of values. up Is the graph wider or narrower than the graph of y = x2-3x +9? What is the y-intercept? ) -14) (- What is the equation of the axis of symmetry? )( Does the graph have a maximum or minimum? ty) i h wider " I What are the coordinates of the ATertex? 1 1 -if ' S I -ill- "t1- =IN) - "/"" -1 *-k (-1).L.-6- n - 1" :": -I2, 1-4 = Lt 1-4S 2 ji. (2.) 2. - a -LI :- L -2. -LI- -ti AoS X=I IIIIIIIIIIMENN = MIIIMMIIIMENI =EMMEN MIMMIIIIIIIMIN IIIMEMMI MENIMIN M MUNN= / , = = IINIMMIENIMMAIMMI /MME RIIME111111= r MEEM M = MME MENIMIIIRE MEMNON.

5 Hour: Name: Algebra I: Intro to Quadratic Functions and Graphing Part 2 To find the y-intercept, plug in XI: 0 and solve for, 9 To find the x-intercept(s), plug in and solve for X Example: Graph y = 3 x 6 :by finding the x-intercept and y-intercept. 2 Find the x-intercept: 0 3 v 2 6 Tz 1vk i a -3 (Lt D ) 4 Example: Graph y = X2-2x 3 by finding the x-intercept(s) and y-intercept. (0) 3) ut p Find the x-intercept(s): = /1( K 3 o =(K-3)(x+ I) X4-1 =0 x 3 ) X = Find the axis of symmetry: X 7- o( t) i 2;-:2(0-3 A05 X = I II III OM M II I III II UM I I I III =EMI= III MEMO UM MIIMM 111 MI IM MIME= M M MEIN= II MI II III IIIMMIMMIMMIll MMIMMIIIMIMIMMIMMIIIII rna MMUM MO 1MM= ummmiaiuiiiiimiimmomimi M MMewasumum muumma MENOMI /1111MOMMIIMA MOOMMIMI MIMI 14" Zero-Product Property V ( 1) 1-1) What is x if 4. x = 0?

6 Example: Graph y = x2 + 3x 4 by finding the x-intercept(s) and y-intercept. up Find the x-intercept(s): (-4,0) 0)6) (x-tit)(x---/).0 v, (r40/-1) )(-1 =-') NMINMININNIIIIINININI ININN M =111 M = ummunummumommmunm EmmammioNE MIIMIN Find the axis of symmetry: x = = (=1) (-3(1) 9 3 c:2 6-0) Example: Graph y = x2 6x 9 by finding the x-intercept(s) and y-intercept. do w h A Find the x-intercept(s): (- 3) 15) o = o O ( 3)(A4-3) X= -3 Find the axis of symmetry: x /

7 Example: Graph y = x2 25 by finding the x-intercept(s) and y-intercept. Find the y-intercept(0) up Find the x-intercept(s): (5/ (-5( ) AOS X = = M M = M M Find the axis of symmetry: =11111M MEI = = =M IIIMME Example: Graph y = 2x2 12x by finding the x-intercept(s) and y-intercept. (o, Find the x-intercept(s): 0 ( 0) Up A -1- _A\ Find the axis of symmetry: 6,4 3 V OHO

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9 Hour: Name: Algebra 1: Intro to Quadratic Functions and Graphing Worksheet 2 1. y = x2 +3x-28 u p (0 2 g) 2. y = 2x2 5x 3 ty (0 Find the x-intercept(s): (-7 /) ( LI - 3 Find the axis of symmetry: X Find the x-intercept(s): v Find the axis of symmetry: A / ) ( 3 t 5 3. y = x2 3x y=x2-4x+4 14 p 0 10) Find the x-intercept(s): (5/ 0.) t - 7 ) v Find the axis of symmetry: A Find the x-intercept(s):,o) Find the axis of symmetry: At = A I I I I I I I I I I I I I I I I M HI MEN I I I I I I M II M I I I I I I I I I M M I I I I I I I I NI NI III M I E II MI I II I II I II I I MIEEIMIEM IME IMEIMIEME MMITEMMI MME IIMIIMEMEMuuuiIIIMIM JIMMIE MIIIMMIll IMIE EMI= M M = I IMMEIMEIMMI MINEN E MIE / == IIIMIIIIMMEME /111111EMMI , r (7 I 0) 4 1 oiso verfa

10 5, y =x2 +2x GI p )0 Find the x-intercept(s): (Di 6) (-2.1 6) Find the axis of symmetry: X 6. y= x 2 +x+ 6 dowil Find the x-intercept(s): (3 CI) Find the axis of symmetry: X y = 4x2 +12x-7 Find the x-intercept(s): P.) ( 2. Find the axis of symmetry: X , ) I p 8. y = X2 9,,fe (0,0 -c Find the x-intercept(s): E 3 ( 3 6) Find the axis of symmetry: D A \

11 Hour: Name: Algebra 1: Solving Quadratics by Factoring and Taking Square Roots We can use the zero-product property to solve quadratic equations by factoring. The equation must be set equal to zero to use this property. I x Solve by factoring x 63 = 0 (X 9 )(X+7) =-0 -q o X o -Fq 7-7 X Whey) ) ohe J'/ /e qua, 2. x2 7x =30 X2-7X " to)(x+ X-10 0 ia-f3 4_10 +to 3 3 X 1 0 X -= 3 3. x2 +8x+7=-5 x2il.2x (x +)Cx 4-0 7o 4. 3x2 + 9x.= 0 3X (X + = 0 3X X )(2x 7) = x2 15x + 3 = x2 4x X = 6A/- 3X (2 Ai -3) -1 (2 X -3) = o 3X-062X-3) o

12 We can solve quadratic equations by taking the square root of each side if b = 0. Note that when b = 0, there is no middle term. To solve by taking the square root of each side, you must first get x2 by itself on one side. Solve by taking the square root of each side. 7. fx-2 8. x2-5 = x2 = op no real soitt-hoh 11. x+17= x2 +15 = 63 -f5 -IE 3X = S x2-13 =32 4/3 +13 z x2 =-10-2_ X 2_ ) 7- y--

13 Hour: Name: Solve by factoring. Algebra 1: Solving Quadratics by Factoring and Taking Square Roots Worksheet 1. x 2 +2x-15=0 (X+5)(x-3) X-1.5 7,0) K [A/ =-5 ) X r x2-11x+19 = ( 2- /IX 8) X-8.-zo) *3 IA/ =8 4 x=o 4. 7x2 +2x = 0 '7 = 7 X Solve by taking square roots. 5. ix fx = ± 6 6. x2 +5= %;),f x2 +10 = 210 -JO -to T OO Fr'7

14 Solve each equation. 9 7x 2 = x2-6x +3 =3 110 /-eq/ 50/ u-l-fori X(-7)(-6) =0 12. x2-5 = X b 7X " & = 0 X = x2 = x2-14x = -7 f -7/r - x 7 7: 0 7 X1-2X4-1 (1/- 1)(X-1) # 15. 5x2-44x+120=-30+11x -(1 K 4-3o +30-1( A/ SX 2-55 X X.L -11K x2-11= -2 -Ht 4-11 xl = X 0 ) X -6 '=-(3' x 41-

15 Hour: Name: Graphing Quadratic Functions using Intercepts 1. y x2 + 4x - 5 Li p find the y-intercept: ) - 5) Find the x-intercept(s): (-5 0) ( 1 )6) Find the axis of symmetry: X (- 2. y = -x2-4x -3 d0wh (1) ) - 3-) Find the x-intercept(s): (3 to) ) Find the axis of symmetry: X 7:- (- ) 3. y=x2 +x-6 4. y=2x2 +8x+8 (0 - it p Find the x-intercept(s): (-3 o) (c7 0) Find the axis of symmetry: )( ) - 4-) MEMINIMIUM rimeiimiceimee MININE MM mumuirun M /41 111EM M11111 sousommom summiumonimmum NIUMMIM ortmomm INEIMIIM111111/M MIELIRIUMIIMIENNIM g) Find the x-intercept(s): Find the axis of symmetry: X (- A 0) ER1M MUM S Thill =11 11= n M M INIIIMII M IN MIKVAIMEMEN M INIMMIMMIll 1111M MMIEUMM MMEM M M M Lip

16 5, y 3x2 6x cl 0 w ii 6. y= x2 +6x-8 do Lijil Find the x-intercept(s): (0 (- 1 0) Find the axis of symmetry: X E I I A') Find the x-intercept(s): ) 0) Find the axis of symmetry: X 3 =EINEM IIMENIIIIIINNIE EMINIME IMENOMMINIMME MINMEMEN111 MEINIIIIMEMEll I /4 EWEN= II NEMENI MENEM, II MENEM MINN MEMILE IMINENEN MI MENNEN= INIIIIIIMEN EMININEMMIMMEEENIMMIE E y = 2x2 +7x-4 itp Find the axis of symmetry: (o Li) Find the x-intercept(s):, 6) 4 ( (;) v X y = 4x 2-9 (0 CID Find the x-intercept(s): Find the axis of symmetry: NIEL MININEMErmum mummonumummolum WHEIEMIEMIIMEME =r11 MEEMEMINIMMIIIIMENIME ININIEMENINENINII EMENEINIME / = IMMIEMINIONIMIL'ININIMEN INIMME X up t

17 Hour: Name: Graphing Quadratic Functions using Intercepts Part 2 1. y = 4x (0 ) 5) door) Find the x-intercept(s): 2 Q ') (5 ) 2. y = 2x2 4x 30 tip (0) - 30) Find the x-intercept(s): (-3) ()) (5/ 0) Find the axis of symmetry: X 0 Find the axis of symmetry: X = 1 ).25) 3. y:----x2-10x+9 U-p (0) 9) Find the x-intercept(s): ) (I ) Find the axis of symmetry: X 5 bg a's 4. y=x2-64 (01 _61-p Find the x-intercept(s): (- 1, (40) Find the axis of symmetry: X = 0 (0 1 6q) b.31.5,b3 2.7S!D;

18 5. y = x2 8x do w y= x2 +2x+8 dowh f 0) Find the x-intercept(s): (0 1 0) (-K 1 0) Find the axis of symmetry: X (-1 Li 1 1 (01D Find the x-intercept(s): 0.4 Find the axis of symmetry: / it X (-z,6) 7. y = 9x y = x2 6x 9 if p oto h f Find the x-intercept(s): I 0) (-021 0) Find the axis of symmetry: X 0 (0 1-3) fat Find the x-intercept(s): 31 6) Find the axis of symmetry: X = _3 E-31

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