Accelerated Math 1Unit 5 - Fall, 2011

NAME _Graphing Quadratic Functions - Review

W/S #3

Solve the following inequalities algebraically and graphically.

)-\\LXLO

inequality

XL-2or x>Cf2)x2 -7x-18 > 0(X-q';(x + 2..) = Q

X~q \X=-2

3)121112- 60m :s; 0

12Y""1fm - 5)= 0

t'Y1::::: () V"l'I =S

inequality

4)3x2- X -1 0 < 0

(5"-+5 rx- 2.)-::: U,

X~ 5/3 I X=- 2-

5)12x2 + 24x +9 ~ 0 ~ = 'f''--------C' :>) -31 - y..,J(L/)(2-+g)(,+3 =-D 1'2- '-

3 (..2K i-3)K;LX t- I') == 0

X=- -3/2. \x:: - '/~6)2x2 -26x+84 < 0

~ (X 'L._13~;- 4-2)::;0;;, ex-Co'){x-,):=;o

X-:=: 0 )X-,

7)6x2 + 36x > 0 ~~~~CD+J-------jCDcw.·~Co )( (X +c)= 0 - 6 .0

X~D X=--(O

Convert each equation to standard form.

8)y=3(x-2)2 -5

j[X:L_4~+ yJ -)3x. '2. - I 2.)( -f /2 ... - ::,-

J lj =5X2-rJ--X +-'1 J

o inequality

-51, 73inequality

x~ -3/2- 0..- X? -YLinequality

inequality

XL - &; Ov X. > 0inequality

9)y = 2(x + 3)(x -7)

::=. 2lx2 -L/x - 21J

( ~:= ~~2--8x - 4-2

10)y=-3(x+5)2 -8

H =: - 3eX 2-~ 10)( .•..Z. 'SJ - 8

Y ~ -3x'2- - 3()~ - I <) - B

~ -3)(7-_3~83 I

Answer the following questions.2 -10/

11) What is standard form and how do you find the vertex? . :::GlX + b)( +C X-==- /U)...12)What is vertex form and how do you find the vertex? -==Q. (X-h '-+-k. v=- (n. <.. ~13) Describe what the axis of symmetry is and how you know hat the-equation of the axis of symmetry is from

looking at the graph (\Hots" PCVla.foof '" If) h0..1f .14) Does every parabola have x-intercepts? (e~plain) No.::r.f +be pat"fllo()/U (S above.

Jbe Xt141S Q/Jd /)/!:k!.£ u..p J,.f wo(')1- cross +11£ )('-<2.)('(s. (a~ an ellO-mfle) ~15) Is it possible that there would only be one x-;ntercept? (explam)~es ~ whR.n ±b.L ~±-e-¥ '0/

l O"Y"'. )(-~\ ~ • ~16) In graphin a qua~ratic inequality with 2 var!ables, what determines whether to use a ~olid or dotted line?

=-the IO-eWloJ)\ '='1 Wf1n ~ L.. dotted L "2: Sol Ie(. _17) How do you know whe'tller to shade inside or outside of the . . ) ~parabola? Cfuce.. 0.. COrdCX):\..f?1 Me! Shade w~e 1+ is +n.u_ (v)S;olo or ~tC(P ~

18) What are the 3 other names for x-intercepts for a quadratic function? 56 t ut1~s I V1.>6~ t ~

, Find the x-in~;~~;ts (MUST BE WRITTEN AS ORDERED PAIRS!!!)g Oil ¥f :19)y=x2+3x-40 20)y=-2(x+5)2+32 21)y=2(x-4)x+5) rtochoW ~,....

0:::: (X +e1x-s) _D -=- -l(x+s)2--t ~'- X-;:-~ ho~~ ~X~ -~ \}(-::S 32::: - 2(~*'S) -0' Sl>h'~ • 6• - z - 1- ~ , 0) (-'jI 0) '),\r.,,,,,,, ~

•.0 I ~ z: (y:.-r~')l- z.\.f.c.tw ,t i(-8)D) (cS,o) ~~to \l(?c\-S)<- x-:=.-; -q -,)r.t ~

± L\ x: X!-; I X ..o.ftTS II 4\),... j-~~:t" i-\- -=- X. (-1,0)(-'1,0) u .f.t ••••.

Complete the chart for each equation. +-4-+-l-f

? J ...1_-12-22)y=-(x+5)-+1 23)y=-3(x-2)(x+8). 24)y=x-+6x-7 ,,- '2A

vertex (-5, I ) vertex (-3) 75) •. If ('oon vertex (-3)- fro)axis of symm X ~ - S- axis of symm l-=- - 3 OC~_.a." axis of symm X' - - 3

~s _ ~ ~,s rLo~ z.•••... ,' opens up'~in I ~min 1YlCL1C == rz S- ~ U' max/€iliY __ --I./~"<L-----roots --tf and. -to roots d, and - 8 0' 'Y roots -1U/td I

0-= - ()(+s)'Z... + , i'.~,.•_ I :::. - ( v:~S ) 'L ""

I ::: ()u- -s ) L.

!1-=-XtS--5'1.\ -::.)(

25)y = _X2 + 1vertex ( 0 J I )axis of symm X -== 0

~s ~rna in I--=------roots I CLn of - Jvertex form - (x- O);L + I

t)y- -)(~+-t

26)y = _4X2 - 2x + 9 )vertex (- Y<f I 31~axis of symm~-; - ~'io ens Ii.ifiij:.j;;,ma min 37/~roots Y" ~4 .L 2

(llvertex form :=. -1(x t ,,) -t ~

~ use +he V€t'+-~Zvad Fo r mu.lfJ..... 6t.U-don'+ h>~-r

+M ~rhpll\(W

27)y = 6x2 + 5x +7 4:31 \

vertex (-5,1:2- I ) -721./)axis of symm X:::::. -s/, 2-

opens Ufmax~) 1'I3/2.froots - S .:/:'.;.VJi13vertex fomiT2- ,-z-.

Ll :» C, (Xt-2-)1. -f !!:f.}11 , z, ::z-'+

1 228) y = -x -82ff\

Sketch the graph of each function. State the intervals of increase and decrease .....b ~3

'X~ 1P-L\'/\

show 13 pts 29) y = X2 - 6x + 10

r

decreqSQ - a» L. x: -: 0

U1CA-l a SR 0 c: 'X c:::. OJ

Sketch the graph of each quadratic inequality.

30) y>-(x-3)(x+3) 31) y<-2(x-8)2+6

Graph each system of quadratic inequalities.X=- -i~-3 Lj =- (-3)z-tC,(-3)+-£' -z: - \

33)y 2 X2 +6x+8

32)Y>_(X+3)2+2

y > _2X2

y S-X2 -2x X--h -1:.--1- W. - -1..-

~~\"1

Sketch the graph of each of the following.-C:, _-3

'i z.

36) y = X2 - X - 12;

I\R~-;-10 - (-12.)2. -0

'::l ~GJ

35)

Find the average rate of change over the given interval.