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 < 6.

Explanation:

Edge

Answer 2

True options:

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

5. The graph is negative on the entire interval –4 < x < 6.

Explanation:

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

This graph intesects the x-axis at points (-4,0) and (6,0). So, the x-coordinate of the vertex is
`(-4+6)/(2)=(2)/(2)=1`

The y-coordinate of the vertex is

`y=(1+4)(1-6)=5\cdot (-5)=-25`

Hence, the vertex is ar the point (1,-25) - frist option is true, second option is false.

For all
`x<1` the graph is decreasing, for all
`x>1` the graph is increasing. So, third option is false.

The graph is positive (placed above the x-axis) for all
`x<-4` or
`x>6`. This means fourth option is false.

The graph is negative (placed below the x-axis) for all
`-4<x<6`. This means fifth option is true.