quadratic functions
Post on 29-Jun-2015
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Exploring Quadratic Functions
The InterceptsThe given intercepts:
x intercepts=-6,-2
y intercept= -3
The Quadratic Function y=ax2+bx+c
For x=-6
y=a(-6)2+b(-6)-3
For x=-2
y=a(-2)2+b(-2)-3
For x=-6 y=36a-6b-3
Y=-12a+2b+1
For x=-2 y=4a-2b-3
Together Y=-12a+2b+1
y=4a-2b-3
0=-8a-2
8a=-2
a=-1/4
Finding B y=4a-2b-3
0=4(-1/4)-2b-3
0=-4-2b
2b=-4
b=-2
The Function a=-1/4
b=-2
c=-3
y=-1/4x2-2x-3
Getting the Graph X=-b/2a
x=2/-1/2
x=-4
y=1
Vertex (-4,1)
Y Pattern- -1/4, -3/4, -1 ¼, -1 ¾, -2 1/4 , -2 3/4 , -3 ¼ , -3 3/4
The Graph
Solve!
y=-1/4x2-2x-3
x=(-b+- b2-4ac )/2a
x=2+- 4-3 /-1/2
2+-1/-1/2
X=-2 or -6
Completing the Square y=-1/4x2-2x-3
x2+8x+12=0
x2+8x+16=4
(x+4)2=4
X+4=+-2
X=-2 or -6
Factoring y=-1/4x2-2x-3
x2+8x+12=0
(x+2)(x+6)=0
X+2=0
X+6=0
X=-2 or -6
Thank You For Watching!
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