CPM Homework Help : INT3 Problem 8-48

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

Step 1:

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

Step 2:

Find the stretch factor by substituting the point.

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

Answer:

Make sure to check your answer.

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