In the xy -plane, the graph of the function `f (x) = x^2 + 5x + 4` has two x -intercepts. What is the distance between the x-intercepts?

Options

A. 1
B. 2
C. 3
D. 4

Answer

C

Explanation

The x-intercepts of the graph of `f(x ) = x^2 + 5x + 4` are the points (x, f (x )) on the graph where f (x ) = 0. Substituting 0 for f (x ) in the function equation yields `0 = x^2 + 5x + 4`. Factoring the right-hand side of `0 = x^2 + 5x + 4` yields 0 = (x + 4)(x + 1). If 0 = (x + 4)(x + 1), then 0 = x + 4 or 0 = x + 1. Solving both of these equations for x yields x = −4 and x = −1. Therefore, the x-intercepts of the graph of `f (x ) = x^2 + 5x + 4` are (−4, 0) and (−1, 0). Since both points lie on the x-axis, the distance between (−4, 0) and (−1, 0) is equivalent to the number of unit spaces between −4 and −1 on the x-axis, which is 3.
Choice A is incorrect. This is the distance from the origin to the x-intercept (−1, 0). Choice B is incorrect and may result from incorrectly calculating the x-intercepts. Choice D is incorrect. This is the distance from the origin to the x-intercept (−4, 0).