# Quadratic Equation Calculus Proof

## Homework Statement

Consider the general quadratic function f(x)=ax2+bx+c with a>0. By calculating the minimum value of this function, show that f(x)$$\geq$$0 for all x if and only if b2-4ac$$\leq$$0

## 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+ax2 but I don't know where to go from there.
Thank You

## Answers and Replies

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You plugged in x=-b/2a wrong... I mean, your formula still shows an x. That shouldn't be there...

Ahh now I see. Thank you