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

A. The vertex of the function is at (1,–25)

E. The graph is negative on the entire interval -4 < x < 6Step-by-step explanation:

Dude above me is right

Answer 2

The vertex of the function is at (1,–25)

The graph is negative on the entire interval -4 < x < 6

Explanation:

we have

`f(x)=(x+4)(x-6)`

This is a vertical parabola open upward

The vertex is a minimum

using a graphing tool

see the attached figure

The vertex is the point (1,-25)

The x-intercepts or roots of the quadratic function are x=-4, x=6

The graph is increasing on the interval x > 1

The graph is decreasing on the interval x < 1

The graph is positive on two intervals ,where x < -4 and x > 6

The graph is negative on the entire interval -4 < x < 6

therefore

The statements that are true are

The vertex of the function is at (1,–25)

The graph is negative on the entire interval -4 < x < 6