Question

The graph of the function f(x) = (x + 2)(x − 4) is shown. On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (1, negative 9), and goes through (4, 0). Which describes all of the values for which the graph is negative and increasing?

Answer 1

The graph of the function f(x) = (x + 2)(x - 4) is a parabola that opens up. The vertex of the parabola is at the point (1, -9), which means the graph is highest at this point. The graph also goes through the points (-2, 0) and (4, 0). To determine where the graph is negative and increasing, we need to consider the intervals of the x-axis where the function values are negative and the slope is positive.

Let's analyze the graph:

From negative infinity to -2: The graph is negative and increasing.

From -2 to 1: The graph is positive and increasing.

From 1 to 4: The graph is positive and decreasing.

From 4 to positive infinity: The graph is positive and increasing.

Therefore, the values for which the graph is negative and increasing are the intervals from negative infinity to -2 and from 4 to positive infinity.

Final answer is The graph of the function is negative and increasing in the intervals from negative infinity to -2 and from 4 to positive infinity.