Question

Write a possible equation for a polynomial whose graph has horizontal intercepts at x = 2, -1/2, -3.

a) (x - 2)(x + 1/2)(x + 3)
b) (x - 2)(x - 1/2)(x - 3)
c) (x + 2)(x + 1/2)(x + 3)
d) (x + 2)(x - 1/2)(x - 3)

Answer 1

The polynomial equation with horizontal intercepts at x = 2, x = -1/2, and x = -3 is (x - 2)(x + 1/2)(x + 3), which corresponds to option a).

Step-by-step explanation:

The student is asking to identify the equation of a polynomial whose graph has horizontal intercepts at x = 2, x = -1/2, and x = -3. The horizontal intercept of a graph, also known as an x-intercept, is where the graph crosses the x-axis. To find the polynomial, we set each intercept x equal to zero, thus the factors of the polynomial are (x - 2), (x + 1/2), and (x + 3).

Therefore, the equation of the polynomial would be a product of these factors:

(x - 2)(x + 1/2)(x + 3).

This corresponds to option a) from the provided choices.