Quad Answers Take Home

Quadratics Take Home
Eue January 3L,2OL4
L.
The equation rJ =F+ 3x - lS in gratrrhed $n ttre set
odsres belcna*
Brrsed u:r this graph, rvhat sre the ronts af the
equation#+5x-18:0?
{I} -$snd6
d2l 0and-tr8
@ s and.-{
t4:l s snd-trS
2.
lHhat a,re the nertes cnd srls of syrnnlehl,' of tLe
prrabola sha,*"n in the diagrem beisnv?
(I,-a); u;is of,strT nruet-ry-: x = I
ts) $erteli: (1,a): atix of $rrfimetfi'; x: -4
@
vm-tex:
t3} l.erter: {-4.11: mfs nf R.rnme[r1':
{43 l.ertesr i-4,I1: ru;is.uf synrnretrl:
r=
r : -4
tr.
3.
The height, E, of a batrl tossed into tlr,e air rtrl be
represented by the equation g : -# + 10x + 3.
$rhere x is th* elrysed tinie. lffhat is tlie equaticu
of the
a:cis
y:5
ts) y: -s
{r}
uf'ry'rnnnehy nf this parabalaP
@ Sr:: S
{.t I
fr: -D
4.
{
$Arirn tearn nnemb,er perfonns a dive from a
-fuct-high spriagbnard. The parab,ola belorv
*ows rbe path of her dir,e,
aE
_E
r
F'r
&
a4FB10
trfirtrnca frqnr Etrlngboard thstl
equation
Xrtlhicih ec
@
{g}
rrpresents tlre aliis of tyn'rrnetrvP
*:s
{3} x: X.3
(a) y=23
s: s
5.
'--*dhicb' is an equntian of the parnbola shown in the
ncconrpmrl,i:r g diagrur rn F
s:-f -2.-+3 tlt=#-g*+s
'yr=#*l:+3
@; =4+l.-+3
tl)
pL
av
JaJ''
f,+
The dingrarn belmr rbmm the grapb of$
l4lhich ftagrarn
shmlrth*E*pltnrfy:
fire
: -d - s.
#
-c7
,nf a parnbola is representecl by the
-Eaph
eqrrati(}n I/ = c.rZ tr{rere a is a prsitive infeger. lf n
is rrutrtipherl h, Z, ttre nerv parabola lvill become
i
I.i
tr.rn-or.rer:
@ nttt**er
nr*crpen danrnrvirrcl
anrl upen upwar<l
tS) wider anrl open eloumrvard
i4) wlder and open uprvard
5TANDARD FORM TO VERTEX FORM
f(*)=
x2 +?x
e (*)13-
9. f (*)=
-3
* rzr'
r *r+il)t
ftq*** i\t = s"?
Sn:n { ":ffJl}l
ft^)
= (x rr)?
10. f (*)=?x2 +t?x
-'{
+5x
FC +3 s r€ +Er'
$*o**#f
Grrl
tL
l
u
(t3+br
*(,),)
rs
c4
=
Az-*tBI
t+,r= = t(-F) '
-t4
r Lr.E t ra y
€
Ccn)* r4t z(P-)
-3
t^
fil= ("nE)'*?
FO.l + t,'|
Fc^) + 14 +
x?
L({fi}7'zz
VERTEX FORM TO 5TANDARD FORM
Lt. f (*) =- (x+3)'+1
- (xl**ptt) + |
Cc*1 * -K? - dor-Q {--f
_C6x;=
^lta *"&f - B
r(*)=z(x -s)' -z
Se$ r, ?- { 5a*A** q
Lz.
)
*b
Flir:. t /? " t?'rtI#-&
= 7t -r?-F f lb
^l
13.
The porent groph of o porobolo hqs undergone the following trcnsformotions. Stote the
eguotion of the new porobolo.
o)
Shifted left 2 down 3 ond reflectedover the x oxis.
b)
Shifted right 3, up 2 and diloted by o foctor of
c)
Shifted left 3, up 5,dilqted by
2.
r.t=
Il-
-
CX+e)1 -3
ffiEs)ufl-
t ond reflected over the x qxis.
-+&*3)
Shifted up 2 ond diloted by 4
4K}
+L
*5
6RAPHIN6 QUADRATIC FUNCTTON5
14.
f,?\
Given
f (*) =3xz - 6x + L
o. Find the oxis of
/T
symme{ry
X=":b=
.
ke
ztub
b. Find the vertex
;
*.ef.? "t*&
Yo"'
.
:
t
t
aplrFl*-+
d1^r_ ^r')
{,Cq=3U}*-bill.
u q'r ft)
c. 6roph f
*\
I
I
:
;
l*). '
:
d. Evoluqt" f^[tl
_
KiJ= "t.'
y' Statethezeros.
f.
o.
- State the
Stote the y-intercePt.
D: C-* ea lrL'. tz,a )
x
€,1)
hFndF:,ff;Fm
\O
a-\
?. &,
0
\
X";:.''
L
?
i4 Lfb = *n
Klry€
i) Find thezeroes round'to thenearest fhousandfh
'{=.
domoin ond Range.
3
It
/F'
-
t-
--- -:1
a -;
K; z"lb
--'F
\,
$lb
4
'-'l
4
r/=
N
tY4t-lI
P,V
I
6"2
I
t0
15.
.liven f
(*) = 2(x = l)a - 3
o. Find the axis of symmetry
,*f)
K3 l
'I
b.
Find the vertex.
, , _V (r ,-3)
c. 6roph
d.
.:'--
-t
:
I
f(*).
Evqluqte
f (t).
Vcrt *
:3
q/. stot"the zeros.
/
l. ,*r" the y-intercept. \
9. Stote the domoin ond ronge.
b'-)
f
h. Find the EXACT zeroes
0 -- ' Q* C**l )'- 3
e -- z C*l)Z-
€\6 (-r F_
=
( *= Li
'[i,
-l
-?
-l
5
ry.
i) Find thezeroes round to the nearest thousandth
"'tI
l
I
t
t= l- ry
/= -.r12{
(= tug
y= 2,zg
of the root.
Compute the discriminqnt ond state the nqture
o. | =-2x2 +4x+3
b.
b? - 4a-e' .
+2-_+
\ b { zu\:-*o
t*F/
o'rcal
* re*[ rffattOnal
t7.
Solve
for the
EXACT roots using completingthe sguqre.
y =(x-l)z +2
o. ! =-2x2 +4x+3
L{
*3
v
= -ut'L {*,b/ .
1-3 * -L c*-LF )
o
it*L(-l)? =*v(* *zs*htl
5 -5 = -l ( x-t)z
-S r--" z L*
Y',
18.
f&
)t*)i'
i
^')t
=
x-f
o
r-J*
-l),
* f.r -r\Z
Solve to the neorest thousqndfh using the guodrotic formulo'
b.
o. ! =-2x2 +4x+3
y =(x-L)z +2
6z,)ac z
,'
Kq *r$g
I
XstrltB
o
Al
rea- t
l'lb
,
t'o