Question

A parabola has x-intercepts of (2, 0) and (-4, 0) and has a leading coefficient of 1. What is the equation of the parabola in standard form? *

Answer 1

9514 1404 393

Answer:

y = x^2 +2x -8

Explanation:

For x-intercepts p and q, factors of the parabola's equation are (x-p) and (x-q). Since the leading coefficient is 1, those are the only factors.

y = (x -2)(x -(-4))

y = (x -2)(x +4) = x(x +4) -2(x +4) . . . . use the distributive property

y = x^2 +4x -2x -8 . . . . use the distributive property again

y = x^2 +2x -8 . . . . . . . .equation in standard form