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 1. The graph is negative on the interval x < - 4.

B. The vertex of the function is at (-3,-16).

C. The graph is increasing on the interval x > - 3.

D. The graph is positive only on the intervals where x < - 7 and where

x > 1.

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 1

Step-by-step explanation:

The roots of this function are the values that make f (x) = 0. As the equation is already factored, we can see that the roots are x1 = 1 and x2 = - 7

The x-coordinate of the vertix can be calculated as:

x_v = (x1 + x2) / 2 = - 6/2 = - 3

So the first statement: "The vertex of the function is at (-4,-15) " is wrong.

The y_coordinate of the vertex is:

f (x_v) = (x_v - 1) * (x_v + 7) = (-3 - 1) * (-3 + 7) = (-4) * (4) = - 16

So the second statemente: "The vertex of the function is at (-3,-16) " is correct.

for values of x greater than x_v = - 3, the graph increases, as the equation represents a parabola with concavity upwards. So the third statement is correct.

As the roots are 1 and - 7 and the concavity is upwards, the parabola have positive values for x1. So the fourth statement is correct.

For values of x< - 4, the parabola can have both positive or negative values (it has positive values for x < - 7) so the fifth statement is wrong.