Question

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

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

Which statement about the function is true?

The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.

Answer 1

Statement 2 is true.

Reason: f(x) = (x+2)(x+6) has zeros at x = −6 and x = −2 and opens upward, so the parabola is negative between its roots. For example, f(−4) = (−2)(2) = −4. Hence f(x) < 0 for −6 < x < −2.