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 nega

Answer 1

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

Reason: f(x) = x^2 + 6x − 7 has vertex at x = −b/(2a) = −6/2 = −3; f(−3) = (−4)(4) = −16. It opens upward (a = 1), so it's increasing for x > −3. Roots are x = −7 and x = 1, so f(x) > 0 outside the interval [−7,1] and f(x) < 0 for −7 < x < 1.