SOLUTION: Find the quadratic function y=a(x-h)^2 whose graph passes through the given points (8,-4), (4,0)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the quadratic function y=a(x-h)^2 whose graph passes through the given points (8,-4), (4,0)      Log On


   

Question 1105122: Find the quadratic function y=a(x-h)^2 whose graph passes through the given points
(8,-4), (4,0)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the graph passes through (4,0), then
0=a%284-h%29%5E2 , so either h=4 or a=0 .
However, if that function is really a quadratic it must be true that
a%3C%3E0 .
Otherwise, the function would just be y=0 .
So , highlight%28h=4%29 .
Substituting that value, and the coordinates of (8,-4), we get
-4=a%288-4%29%5E2
-4=a%2A4%5E2
-4=16a
a=16%2F%28-4%29
highlight%28a=-1%2F4%29
Three quadratic function is
highlight%28y=%28-1%2F4%29%28x-4%29%5E2%29 or highlight%28y=-%28x-4%29%5E2%2F4%29 .