Question

The graph of the function f(x) = (x − 3)(x + 1) is shown. On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0). Which describes all of the values for which the graph is positive and decreasing? all real values of x where x < −1 all real values of x where x < 1 all real values of x where 1 < x < 3 all real values of x where x > 3

Answer 1

A: all real values of x where x < −1

Explanation:

On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).

Answer 2

Correct option: first one -> all real values of x where x < −1

Explanation:

First we need to find the roots of the function f(x):

0 = (x - 3)(x + 1)

(x - 3) = 0 -> x = 3

(x + 1) = 0 -> x = -1

The roots of the function are x = 3 and x = -1.

The vertex is between the roots (x = 1) and has a negative value of y (y = -4), so the concavity of the parabola is upwards.

So the graph is decreasing until it reaches the vertex, then the graph is increasing.

Then, we can affirm that the graph is positive and decreasing for all real values of x where x < -1 (for x > -1 and x < 3 we have negative values)

Correct option: first one