Question

Describe the shape of the graph of f(x) = (2x - 3)(x+6) at the x-intercepts.

A. The graph bounces off the x-axis at (1.5, 0) and at (-6, 0).

B. The graph crosses the x-axis at (1.5, 0) and bounces off the x-axis at (-6, 0).

C. The graph crosses the x-axis at (1.5, 0) and at (-6, 0).

D. The graph bounces off the x-axis at (1.5, 0) and crosses the x-axis at (-6,0).​

Answer 1

The graph of f(x) = (2x - 3)(x + 6) is a parabola that crosses the x-axis at the points (1.5, 0) and (-6, 0), making option C the correct answer.

Step-by-step explanation:

The graph of the function f(x) = (2x - 3)(x + 6) is a parabola because it is a polynomial of degree 2. To determine the behavior of the graph at the x-intercepts, we need to find the roots of the equation by setting f(x) to zero. Doing so gives us the roots x = 1.5 and x = -6.

Since both factors are linear and don't have even multiplicities (such as a square or higher even power), the graph will cross the x-axis at both intercepts. Therefore, the correct answer is C. The graph crosses the x-axis at (1.5, 0) and at (-6, 0).