Question

Which statement about f(x) = x^2 + 16x + 3 is true

A. The function has a maximum value of 3
B. The function has a maximum value of 16
C. The function has a minimum value of -8
D. The function has a minimum value of -61

Answer 1

D

Explanation:

Given a quadratic function in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

• If a > 0 then minimum value

• If a < 0 then minimum value

For

f(x) = x² + 16x + 3

a = 1 > 0 then f(x) has a minimum value

The minimum is the value of the y- coordinate of the vertex.

The x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

Here a = 1 and b = 16 , then

`x_(vertex)` = -
`(16)/(2)` = - 8

To find the y- coordinate of the vertex, substitute x = - 8 into f(x)

f(- 8) = (- 8)² + 16(- 8) + 3 = 64 - 128 + 3 = - 61

Thus the function has a minimum value of - 61 → D