Question

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

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?

The function is increasing for all real values of x where
x < –4.
The function is increasing for all real values of x where
–6 < x < –2.
The function is decreasing for all real values of x where
x < –6 and where x > –2.
The function is decreasing for all real values of x where
x < –4.

Answer 1

The first statement is true.

Reason: the parabola opens downward and has its maximum (vertex) at x = -4, so f increases on (-∞, -4) and decreases on (-4, ∞). Thus f is increasing for all real x with x < -4.