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

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