Question

The graph of the function f(x) = –(x + 3)(x – 1) is shown below.

On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0).

Which statement about the function is true?

The function is positive for all real values of x where
x < –1.
The function is negative for all real values of x where
x < –3 and where x > 1.
The function is positive for all real values of x where
x > 0.
The function is negative for all real values of x where
x < –3 or x > –1.

Answer 1

The second statement is true.

Reason: f(x)=-(x+3)(x-1) has zeros at x=-3 and x=1 and opens downward, so it is positive between the roots (-3<x<1) and negative outside them (x<-3 and x>1).