Question

Determine the vertex form and the maximum or minimum value of the function.

f(x)=2x2+8x+3

A f(x)=2(x+4)2-13, the maximum value of fis -13

Bf(x)=2(x+4)2 -13, the minimum value of fis -13

f(x)=2(x+2)2-5, the maximum value of fis -5

D f(x)=2(x+2)2-5, the minimum value of fis -5

Answer 1

Complete the square:

f(x) = 2x^2 + 8x + 3
= 2(x^2 + 4x) + 3
= 2[(x+2)^2 - 4] + 3
= 2(x+2)^2 - 8 + 3
= 2(x+2)^2 - 5.

Since the coefficient 2 > 0, the parabola opens upward, so it has a minimum value -5 at x = -2.

Correct choice: D.