Quadratic Equation Calculus Proof

  • #1

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)[tex]\geq[/tex]0 for all x if and only if b2-4ac[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+ax2 but I don't know where to go from there.
Thank You
 

Answers and Replies

  • #2
22,089
3,286
You plugged in x=-b/2a wrong... I mean, your formula still shows an x. That shouldn't be there...
 
  • #3
Ahh now I see. Thank you
 

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