What is the range of the function y=2x^2 +32x - 4?

1 Answer
turksvids
Jan 17, 2018

y>=-132

Explanation:

This a quadratic function with positive leading coefficient so it has a minimum value at its vertex. The vertex of y=ax^2+bx+c is (h,k) where h=-b/(2a) and k is found by substitution.

For the given function h=-32/(2*2)=-32/4=-8.

Find k by substitution:

k= 2(-8)^2+32(-8)-4

k= 128-256-4
k=-132

Since the minimum is (-8,-132) and there is no maximum value, the range of the function is y>=-132.

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