Question

The graph of the function f(x) = –(x + 6)(x + 2) is shown below.

need answer asap

On a coordinate plane, a parabola opens down. It goes through (negative 6, 0), has a vertex at (negative 4, 4), and goes through (negative 2, 0).


Which statement about the function is true?


A. The function is increasing for all real values of x where

x < –4.

B. The function is increasing for all real values of x where

–6 < x < –2.

C. The function is decreasing for all real values of x where

x < –6 and where x > –2.

D. The function is decreasing for all real values of x where

x < –4.

Answer 1

Option A. x < -4

Explanation:

The given function is f(x) = -(x + 6)(x + 2)

General form of the function will be,

f(x) = -(x² + 2x + 6x + 12)

= -(x² + 8x + 12)

Vertex form of the function will be,

f(x) = -[x² + 2(4)x + 12]

= -[(x² + 2(4)x + 16) - 16 + 12]

= -(x + 4)² + 4

Therefore, parabola for the function above will open down with vertex (-4, 4) as shown in the graph attached.

Graph shows the function is increasing in x < -4 and decreasing in x > -4.

Therefore, Option A. is the correct answer.