Answer:
f(x) = x² + 11x - 26
Step-by-step explanation:
Given the zeros of a quadratic function, x = 2 and x = -13, which are the x-intercepts or the roots that are the solutions to the function that they represent. They are also referred to as the zeros of the function.
In order to determine the quadratic function using the x-intercepts, use the Zero Product Property Rule, where it states that, if a and b are real numbers, with a·b = 0, then it means that a = 0 or b = 0 or both. In other words:
(x - 2) = 0 and (x + 13) = 0
(x - 2) (x + 13) = 0
Use these binomial factors and perform the FOIL method to establish the quadratic function:
f(x) = (x - 2) (x + 13)
f(x) = x² + 13x - 2x - 26
Combine like terms:
f(x) = x² + 11x - 26
Therefore, the quadratic function is f(x) = x² + 11x - 26.
