Question

How does the zero product property help you find the x-intercept of y = x² - x - 12?

Answer 1

An \(x\)-intercept is a point on a curve of the form \((x,0)\). In terms of the equation, you let \(y=0\), then solve for \(x\):
\[0=x^2-x-12~~\Rightarrow~~0=(x-4)(x+3)\]
The zero product property tells you that you get
\[\begin{cases}x-4=0\\x+3=0\end{cases}\]