Question 292352: How would I write a quadratic equation in standard form that passes through the points (-2,-2), (0,-6), (4,-2)?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! How would I write a quadratic equation in standard form that passes through the points (-2,-2), (0,-6), (4,-2)?
:
Using the form: ax^2 + bx + c = y
:
c = y intercept (when x=0) therefore c = -6
:
Two equations
x=-2,y=-2
(-2^2)a - 2b - 6 = -2
4a - 2b = -2 + 6
4a - 2b = 4
and
x=4,y=-2
(4^2)a + 4b - 6 = -2
16a + 4b = -2 + 6
16a + 4b = 4
:
Multiply the 1st equation by 2, add to the above equation
16a + 4b = 4
8a - 4b + 8
-------------------- eliminates b, find a
24a = 12
a = 
a = .5
:
Find b, using the 1st equation
4(.5) - 2b = 4
2 - 2b = 4
-2b = 4 - 2
b = 
b = -1
:
The equation: y = .5x^2 - x - 6; in standard form
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