Finding Maximum Value of Quadratic Polynomials

[msu_math]

Problem: What is the maximum value of -x² + 4x + 10?

Solution: At first we rewrite the given polynomial in the form "a perfect square + constant". Here, -x² + 4x + 10 = - (x-2)² + 14 . Since squares are non-negative, - (x-2)² + 14 <= 14. Thus, the maximum value of the quadratic is 14, which is achieved for the minimum value of (x-2)² i.e. for (x-2)²=0 or at x=2.

[Nargis Akter]

Thanks for sharing.