Question

How does the zero product property help you find the x intercept of y=x^2-x-12?

Answer 1

We first factor this quadratic.  We want factors of c, -12, that sum to b, -1; -4(3) = -12 and -4+3 = -1, so those are the two we will use:
y=(x-4)(x+3)

The zero product property tells us that in order to get a product of zero, one of the factors must be zero.  This means either x-4=0 or x+3=0.  We solve both of these equations to find the roots, or x-intercepts:
x-4=0
x-4+4=0+4
x=4

x+3=0
x+3-3=0-3
x=-3