Write an equation of the parabola in intercept form with x-intercepts of -16 and 2

Answer 1

Since you already have the x-intercepts, you really just need to place each intercept into it's binomial then multiply them. To do this, take each intercept and re-arrange it so you get a binomial that is set equal to 0. Example:

x = 2 ---- Subtract 2 from both sides

x - 2 = 2 - 2

x - 2 = 0

Do the same for -16

x = -16 ---- Add 16 to both sides

x +16 = -16 + 16

x +16 = 0

Now you have your two binomials, (x - 2) and (x + 16). Multiply these. The FOIL method is common; F(irst), O(uter), I(nner), L(ast).

F O I L

(x - 2)(x + 16) = (x * x) + (16 * x) + (-2 * x) + (-2 * 16) = x^2 + 16x - 2x -32.

Combine like terms (bolded).

x^2 +14x -32

This equation gets you the intercepts of -16 and 2.