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

Explanation:

just took the test

Answer 2

Real values of x where x < -1

Explanation:

Above the x-axis, the function is positive.

The function is decreasing when the gradient is negative.

The function has a positive

`{x}^(2)`

coefficient, therefore the vertex is a local minimum;

This means the gradients are negative before the vertex and positive after it;

To meet the conditions therefore, the function must be before the vertex and above the x-axis;

This will be anywhere before the x-intercept at x = -1;

Hence it is when x < -1.