Question

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.



Which statements about the function are true? Select three options.

The vertex of the function is at (–4,–15).
The vertex of the function is at (–3,–16).
The graph is increasing on the interval x > –3.
The graph is positive only on the intervals where x < –7 and where
x > 1.
The graph is negative on the interval x < –4.

Answer 1

True statements:
- The vertex of the function is at (–3, –16).
- The graph is increasing on the interval x > –3.
- The graph is positive only on the intervals where x < –7 and where x > 1.

Reason: f(x) = (x−1)(x+7) = x^2 + 6x − 7 has vertex at x = −b/(2a) = −6/2 = −3, f(−3) = −16. Since a = 1 > 0 the parabola opens upward (increasing for x > −3). Roots are at x = −7 and x = 1, so f(x) > 0 for x < −7 and x > 1 and f(x) < 0 for −7 < x < 1.