SOLUTION: Express f(x)= -4x^2+40x-13 into f(x)=a(x-h)^2 + k and find the vertex of this quadratic function. I'm at a loss on where to begin and what to do, could someone more intelligent th

Algebra ->  Functions -> SOLUTION: Express f(x)= -4x^2+40x-13 into f(x)=a(x-h)^2 + k and find the vertex of this quadratic function. I'm at a loss on where to begin and what to do, could someone more intelligent th      Log On


   

Question 519109: Express f(x)= -4x^2+40x-13 into f(x)=a(x-h)^2 + k and find the vertex of this quadratic function. I'm at a loss on where to begin and what to do, could someone more intelligent than I am, please give me an example to follow?
Thanks so much!!! :)
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
this ain't rocket science ___ make the equation look like the general form

separate the constant term ___ f(x) = -4x^2 + 40x .... -13

factor ___ f(x) = -4(x^2 + 10) .... -13 ____ starting to look like something?

now the "tricky" part - complete the square ___ f(x) = -4(x^2 + 10x + 25) + 100 .... -13
___ you complete the square by taking half of the x-term coefficient, squaring it and adding it
___ the "trick" is that the square you are completing is being multiplied by a value (-4)
___ to avoid changing the overall value of f(x), you have to balance the extra -100 (the -4 times 25) by adding 100

writing in vertex form ___ -4 (x + 5)^2 + 87