SOLUTION: A quadratic formula satisfies f(x) bigger than or equal to 0 for all x . If f(1)=0 , f(3)=3, then find f(5)

Algebra ->  Equations -> SOLUTION: A quadratic formula satisfies f(x) bigger than or equal to 0 for all x . If f(1)=0 , f(3)=3, then find f(5)       Log On


   

Question 839626: A quadratic formula satisfies f(x) bigger than or equal to 0 for all x . If f(1)=0 , f(3)=3, then find f(5)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since f(1)=0, the vertex occurs at x=1.
f%28x%29=a%28x-1%29%5E2
f%283%29=a%283-1%29%5E2=3
4a=3
a=3%2F4
So then,
f%28x%29=%283%2F4%29%28x-1%29%5E2
f%285%29=%283%2F4%29%285-1%29%5E2
f%285%29=%283%2F4%29%284%29%5E2
highlight%28f%285%29=12%29