Question

Given x-intercepts of 2 and -8 and that it passes through (-6,-4), what is the equation of the quadratic function?

A) y = 4(x - 2)(x + 8)
B) y = -4(x + 2)(x - 8)
C) y = (x - 2)(x + 8)
D) y = -4(x + 2)(x - 8)

Answer 1

The quadratic equation of the function with the given characteristics is y = (x - 2)(x + 8), making the correct answer C.

Step-by-step explanation:

The quadratic equation of a function with x-intercepts at 2 and -8 and passes through the point (-6,-4) can be determined by the form y = a(x - r)(x - s), where 'r' and 's' are the roots of the quadratic equation, and 'a' is a constant that needs to be found. Knowing the x-intercepts, we can write the equation as y = a(x - 2)(x + 8). After that, we substitute the value of the point (-6,-4) into the equation to solve for 'a': -4 = a(-6 - 2)(-6 + 8), which simplifies to -4 = a(-8)(-4). Therefore, a = 1 and the correct answer is C) y = (x - 2)(x + 8).