### Home > A2C > Chapter 9 > Lesson 9.1.3 > Problem9-58

9-58.

Write a polynomial equation for a graph that has three x-intercepts: $\left(−4, 0\right)$, $\left(1, 0\right)$, and $\left(3, 0\right)$, and passes through the point $\left(−1, 60\right)$.

Start by writing an equation with those interceptsusing the Zero Product Property.
$y = a\left(x + 4\right)\left(x − 1\right)\left(x − 3\right)$

Find the stretch factor by substituting the point.

$(60) = a((−1) + 4)((−1) − 1)((− 1) − 3)\\60 = a(3)(−2)(−4)\\60 = a(24)\\ a=\frac{5}{2}$

$y=\frac{5}{2}(x+4)(x-1)(x-3)$