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Finding Maximum Value of Quadratic Polynomials

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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.

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