Help with precalculus equation.

Question

Can someone please help me with solving this equation?

The function f(x)=2x^2+16x+3 has a minimum of ______?

Answer 1

Put the quadratic into vertex form:

1) divide through by 2: f(x) = 2(x² + 8x + 3/2)

2) complete the square: f(x) = 2(x²+8x+16 -16+3/2) = 2((x+4)²-29/2)

3) f(x) = 2(x+4)² - 29 so min is at x = -4 and f(-4) = -29

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