Question

In the xy-plane, the graph of the quadratic function g intersects the x-axis at x = 5 and x = 9. Which of the following could be an equation of g?

A) g(x) = (x - 5)(x - 9)
B) g(x) = (x + 5)(x + 9)
C) g(x) = (x - 7) + 4
D) g(x) = (x + 7) + 4

Answer 1

The equation of the quadratic function g that intersects the x-axis at x = 5 and x = 9 is g(x) = (x - 5)(x - 9).

Step-by-step explanation:

The subject of this question is a quadratic function g which intersects the x-axis at x = 5 and x = 9. The quadratic function that would satisfy this condition is g(x) = (x - 5)(x - 9), because these factors become zero when x is equal to 5 and 9, respectively, indicating the points where the graph intersects the x-axis. Options B), C), and D) do not represent quadratics that intersect the x-axis at these given points; Option B) represents a quadratic that intersects at negative points, while Options C) and D) are not even quadratics but linear functions - they cannot intersect the x-axis at more than one point.