Quadratic Equation Calculus Proof

[harrietstowe]

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)\geq0 for all x if and only if b²-4ac\leq0

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

 

[micromass]

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

 

[harrietstowe]

Ahh now I see. Thank you