graphing parabolas and circles - wordpress.com · 2017-05-12 · graphing parabolas and circles...

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Graphing Parabolas and Circles Parabolas y = ax 2 + bx + c a > 0 Concave up (smiling) Vertex is a minimum: x = !" #$ , find y by plugging in Axis of symmetry: x = !" #$ Intercepts: (0, c) (x1, 0) and (x2, 0): Find by factoring or quadratic formula a < 0 Concave down (frowning) Vertex is a maximum: x = !" #$ , find y by plugging in Axis of symmetry: x = !" #$ Intercepts: (0, c) (x1, 0) and (x2, 0): Find by factoring or quadratic formula Tv Iii '±÷ A

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Page 1: Graphing Parabolas and Circles - WordPress.com · 2017-05-12 · Graphing Parabolas and Circles Parabolas y = ax2 + bx + c a > 0 Concave up (smiling) Vertex is a minimum: x = !",

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

Page 2: Graphing Parabolas and Circles - WordPress.com · 2017-05-12 · Graphing Parabolas and Circles Parabolas y = ax2 + bx + c a > 0 Concave up (smiling) Vertex is a minimum: x = !",

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

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:•i×=o : y= -8 ( 0 , -8 ) ✓

y=O : 0=14-2×-8

War Parabola°=⇐4Kxnt¥hI¥E,o,Vekx :*

.hat 4 ,'¥a¥

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Page 3: Graphing Parabolas and Circles - WordPress.com · 2017-05-12 · Graphing Parabolas and Circles Parabolas y = ax2 + bx + c a > 0 Concave up (smiling) Vertex is a minimum: x = !",

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 ...

Page 4: Graphing Parabolas and Circles - WordPress.com · 2017-05-12 · Graphing Parabolas and Circles Parabolas y = ax2 + bx + c a > 0 Concave up (smiling) Vertex is a minimum: x = !",

3)x=y2–6y+5

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Page 5: Graphing Parabolas and Circles - WordPress.com · 2017-05-12 · Graphing Parabolas and Circles Parabolas y = ax2 + bx + c a > 0 Concave up (smiling) Vertex is a minimum: x = !",

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

Page 6: Graphing Parabolas and Circles - WordPress.com · 2017-05-12 · Graphing Parabolas and Circles Parabolas y = ax2 + bx + c a > 0 Concave up (smiling) Vertex is a minimum: x = !",

2)Graph(x-1)2+(y+2)2=9

3)Graphx2+y2–4x+2y-11=0

yCircle : hardy ' ^

Center :( I ,-2)

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Page 7: Graphing Parabolas and Circles - WordPress.com · 2017-05-12 · Graphing Parabolas and Circles Parabolas y = ax2 + bx + c a > 0 Concave up (smiling) Vertex is a minimum: x = !",

* 0 : y2+4y-4=Op

y= -4542=4×1

=- 4±F6÷

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4+-4+2

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= - Ztzk - 2- zfa

a 0.8284 . ..

X - 4.828427 ...

Page 8: Graphing Parabolas and Circles - WordPress.com · 2017-05-12 · Graphing Parabolas and Circles Parabolas y = ax2 + bx + c a > 0 Concave up (smiling) Vertex is a minimum: x = !",

Finns ( * , )t+a+z5=9XHXH+4=9×2.2×+5--9

1/2-2×-4=0

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=2±2A = 25

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