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## Homework Statement

Consider the general quadratic function f(x)=ax

^{2}+bx+c with a>0. By calculating the minimum value of this function, show that f(x)[tex]\geq[/tex]0 for all x if and only if b

^{2}-4ac[tex]\leq[/tex]0

## Homework Equations

## The Attempt at a Solution

I know that the min for a quadratic equation is at x=-b/2a and I proved this by taking the derivative of f(x) and setting it equal to zero. I then plugged this in for x to get c+ax

^{2}but I don't know where to go from there.

Thank You