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).
AO
The graph is increasing only on the interval -4< x < 6
The graph is positive only on one interval, where x <
4.
6
-
The graph is negative on the entire interval
4

Answer 1

True options:

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

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

Step-by-step 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 \dfrac{-4+6}{2}=\dfrac{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.

hope this helps homie