Question

Part of the graph of the function f(x) = (x + 4)(x – 6) is shown below.



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

The vertex of the function is at (1,–25).
The vertex of the function is at (1,–24).
The graph is increasing only on the interval −4< x < 6.
The graph is positive only on one interval, where x < –4.
The graph is negative on the entire interval
–4 < x < 6.

Answer 1

True: "The vertex of the function is at (1,–25)." and "The graph is negative on the entire interval −4 < x < 6."

Reason: f(x) = (x+4)(x−6) = x^2 − 2x − 24 has vertex at x = −b/(2a) = 1, and f(1) = 1 − 2 − 24 = −25. The roots are x = −4 and x = 6, and since the parabola opens up, it is negative between the roots (−4, 6) and positive outside them.