SOLUTION: Write the function in the form f(x)=a(x-h)^2+k by completing the square . F(x)=x^2+16x-9

Algebra ->  Functions -> SOLUTION: Write the function in the form f(x)=a(x-h)^2+k by completing the square . F(x)=x^2+16x-9      Log On


   

Question 969084: Write the function in the form f(x)=a(x-h)^2+k by completing the square . F(x)=x^2+16x-9
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the function F%28x%29=x%5E2%2B16x-9 in the form f%28x%29=a%28x-h%29%5E2%2Bk will be:
F%28x%29=%28x%5E2%2B16x%29-9....recall the rule:a%5E2%2B2ab%2Bb%5E2=%28a%2Bb%29%5E2
when you compare it to your function, you can see that a=1 and 2ab=16
since we need b to complete the square, we can calculate it from 2ab=16
=>b=16%2F2a=>b=16%2F%282%2A1%29=>b=16%2F2=>b=8
so, we add and subtract b%5E2=8%5E2
F%28x%29=%28x%5E2%2B16x%2B8%5E2%29-8%5E2-9
F%28x%29=%28x%2B8%29%5E2-64-9
F%28x%29=%28x%2B8%29%5E2-73 where h=-8 and k=-73;so, vertex is at (-8,-73)