Name:

C \ *?- -:\ L

-\ *'l- 0

Period:

SolvinB & Craphing Polynomials Practice

d z L)--t--l-lr\t -1_ -\o -\u-\ -5 -t -q

!(x\ = (x -! ( xt\) [-x" - \'r' -'{}!tx\ = - (.t--t\tXcr\ (12+\^'r +$)

1 Sketch a graph of the given polynomial. lnclude all intercepts and end-behavior in your sketch. Youmay want to make a sign chart to determine when the functions is above and below the x-axis. Makesure to scale and label your graph!

a. P(x) : (r + 5)(x - L)(x + 2)

'r-'lli

i--{I

b. f(x)= -x2+2x-L{lU

= - (rt- -Lx + \)

D(x\ = (x-r) (x-t) [^*+t

d. g(x) : -x4 - 3x3 + 2x2 + LZx * Iu

I I

1 J*"i

x

!(x\=[x-\)(x'-x-2)

P(x)-x3-zxz*x*2

-t t\--5-::.*J

e. P(x)=2x3-3x2-3x*2

x

L -n -1 -?-

..U ,\ -z -tLr-\0!(x\ = (x-r\[r_ryJ n 1(-\)

P(x) - (*' + L)(x.- 3)(r + 1)

ctb' P(x)=x4-4x3*7x2 *L6x*LZ

A(x\ = (x-r)(x-t\(x \1+

i)(x -r

h. P(x):-x4*x3+7x2*x-6I

p (x\ = .= (x-r\(rt +\)(x

tU-:1}-JL.1"10\t*\ _T 5 L

\-3 q -\t 0 \o\ldp(x\ = (x *\](x- t) ( x' +t\)

\.

ntt*i=-to -\\ (^( + t) (ir.t-+ x - t)

+'r> ) \.-d-

\

2. Put each quadratic equation into vertex form. Then, determine the maximum or minimumvalue of the function.

a. f(x)--2x2*4x-3._ txt +\^( -b = 0

t-l -i-?-xa+'{x e n

*"1(x" -'?-x * l-) = 3 * taX!-1(x-\)' = i + (-*L)

- l(x *\)' ' \

S(.d = -'l(x*\)' -\\ev\er( .I t, -t)

\\axrtnr\w^r \a\'*e ' *\

b. g(x)-x2+3x-Lx'+tx-\ =\

r\ +\-(a+lx * y*

(x+ sh)- ''a. -t'- k(x + c/r; *

-a1(x) = (x +31r.,i

\eT \ex . (-

\\rfirrfiU,ff\ ta\Ue ' "l?lq

=\+%u7* + q/s

\34

- rslq1^ , 1./, ,- "/q )

c. h(x):-x2-2x*5

-*-tx\5 =o::i-x2-ax = -E'J

- (xtr 'lx + J*) = "b-(x+tt* -t

h(x\=-(xq\\'q-Llev\ex' (-\) t)

Mqx\rnuy.ft \a\ur,e

("\ i t *L-)

f(x) - 3x2 -9x * l03xt_tx r\0 =0\! -\s

3x'-tx = -\satj(x'-3x tT-\ =

3 (x - zl'\' = -s\/q. ^,r? -te/qa1** a/z) :-

\(x\= 1(-r- t/r)'\ ev \e 1 ' ('1'''

d.

-\b r ,, (14)r r/q

!2- ,.\ '1\R/u)

\\rnr\nnurn \ a\ue ' ij /q

.t

3. Factor each polynomial completely. Then, list all complex zeros.

a. P(x) - xs -3xa *2x3 - 6x2 * x - 3

Go= *3 tac\oxt" \.,t^ - \ qac\ox"o \\5

pLri";\\;\€ ret \E t\ , t Ia\ \ -3 L -b \ aJ\- rt'3 o b o 7

P(x\ -- (x-t) (xq " tx'+\)P(x\= (x-t')(tt+\)' r1p (x\ = (x-3)(x- r.)" (-x+,t )-

aeYot'.3)l' )-/\'

b. P(x) - x3 - Zxz - L3x - Lo

O6 = -\O \actovt'. \, t)t )\Ort - \ \ac\ox'o \\ 3*p otAlu\e x *tr\ t . !\ , t-L, t% )"l\il-\ \ \ -L -\t -\CIv -\ n \offi

P[x\ = (x * t) (x' *bx -\0iQ(x) = (x\\) (t-b\ t:l *'z\

zeY$t . *\ 5 "L

c. P(x) - x4 +Sxz + 4

P("v.) = (x'* \-) (r" + q)

! (x\ = (r-i\(x + ^Xx

*t-'t){.rr *tt )

a.QYOt , -,\. ,l.-l-

,^,*L/\

d. P(x) - x4 - 8x3 * 2ox2 - 32x * 640o = 6\ Qac\ovt', \., ?-,\ .,81 \U,11Gr\*\ Qaq\bvt \po\si\\e ro o \\"L\ ) t'1-) $ )tt"Trb:-{' :t

\\\ -t 1-\ 'iz 6qT--t{ l1^ *

""r.+\-uq-\uoq\ \ -+ q -\u

-

vq 0 \bffia (x) =- (x r\\' (x1 {qJp(x\ = tx -\)' (1. +-r,.)(x-Z+ :

?evux'. \) 'Li : *?""t

1.