I have this polynomial in factored form that is already transformed:
f(x) = $a(x-b)^2(x-c)$, where a,b,c are real constants
This function is then transformed to a new function g(x), the following transformations were applied to function f(x):
1) reflected in the x-axis
2) Horizontally stretched by a factor of 1/2
3) Horizontally translated 3 units to the right.
After these transformations the new function g(x), the graph of g(x) goes thru the following points:
1) (-5,0)
2) (3,64)
3) (7,0)
FIND the values of a,b and c of the original function f(x)! End of Question
I tried to just plug in the points and then i would have a system of equations to solve. BUT it seems really difficult to solve these because the equation is non-linear. SO I am guessing that there must be another way. I can't think of what the other way could possibly be.
Here is my g(x) function:
g(x) = $-a(0.5(x-b)-3)^2(0.5(x-c)-3)$ // Hope i got this part right
Hope someone out there can help out here.