graphing parabolas and circles - wordpress.com · 2017-05-12 · graphing parabolas and circles...
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GraphingParabolasandCircles
Parabolasy=ax2+bx+ca>0Concaveup(smiling) Vertexisaminimum:x=!"#$ ,findybypluggingin Axisofsymmetry:x=!"#$ Intercepts: (0,c) (x1,0)and(x2,0):Findbyfactoring
orquadraticformulaa<0Concavedown(frowning) Vertexisamaximum:x=!"#$ ,findybypluggingin Axisofsymmetry:x=!"#$ Intercepts: (0,c) (x1,0)and(x2,0):Findbyfactoring
orquadraticformula
TvIii
'±÷A
Ex:Foreachofthefollowing: • Plotatleast4pointstograph• Labelallintercepts• Labelthevertex• Specifytheaxisofsymmetry 1)y=x2-2x-8
2)g(x)=-3x2-9x-2
Quadtrmda : ×=tb#h4aZa
EgoAFvertex : xiben÷ ←
.fi#=2==1=x- i
¥Ei¥:.ae:}- i
( i , - 9)a
:•i×=o : y= -8 ( 0 , -8 ) ✓
y=O : 0=14-2×-8
War Parabola°=⇐4Kxnt¥hI¥E,o,Vekx :*
.hat 4 ,'¥a¥
tE⇒×I¥±±.it#sxgkj=-stZI9EehZ• Co
, -4
= -2÷+¥ -2
v
= - ¥+5,1 .
,±=¥=¥x⇒g6b-2
.co,
. 2) →
4=0 gcD= - 3×2-9×-2
0=-3×2-9×-2
x=-b±#MZa
= -fa)±rEyc→E#- 3)
= 9± six±esta
=9±r¥or9⇒t= - 2.7583
...
or -0.24169 ...
3)x=y2–6y+5
=±a=!f=3 ^ ( 5,6 )
×IFdkttE+
•#a¥m←.ie#hTIsy=O:X=0t60t5-4
X=5 ( 5,0 )
×% =yt6yt50=(-1-574-1)y=5 ,
1
co ,5) ( on )
Circlesx2+y2=r2 (StandardForm) Centerat(0,0) Radius=r Diameter=2r Interceptsat: (0,r) (0,-r) (r,0) (-r,0)(x-h)2+(y-k)2=r2 (StandardForm) Centerat(h,k) Radius=r Diameter=2r FindInterceptsbypluggingin x=0andy=0 Graphbyfindingthecenterandthen plottingtheradiusup,down,
leftandright1)Graphx2+y2=9
y
Circle+y2=r2
radius =3( 0,3 )
Center ( 9 ;oP§?tו
2)Graph(x-1)2+(y+2)2=9
3)Graphx2+y2–4x+2y-11=0
yCircle : hardy ' ^
Center :( I ,-2)
Tinnitus'd;ott¥r#r•.¥←¥f±untamed.EE, !,
'
a.4€e¥×1+42+4×+4=9 -2 -2k
•• ( c , -5 )
y2+4y +5=9- 9 - 9 ✓
ft44
-X ?±xtykzy= 11 ^
¥Esf:H§T4,3 )
~ •
9¥€¥EHxH¥.EE#:*ti.f.HYCenter:( 2
,-1 ) Hit )
.
Radius = 4 .
✓•
( 2 , -5 )
* 0 : y2+4y-4=Op
y= -4542=4×1
=- 4±F6÷
⇒zt KEER⇐F
= -
4+-4+2
=2f2±=K)= - 2±zf
= - Ztzk - 2- zfa
a 0.8284 . ..
X - 4.828427 ...
Finns ( * , )t+a+z5=9XHXH+4=9×2.2×+5--9
1/2-2×-4=0
×=2±Xht4÷2 . 1
=2±y±⇐of reX
=2±2A = 25
¥It.I±F= HA .r IF
I 3.2 . . . -1.236 ..