### Home > A2C > Chapter 12 > Lesson 12.1.3 > Problem12-52

12-52.

A polynomial graph has a double root at $\left(−2, 0\right)$, a single root at $\left(2, 0\right)$, and passes through $\left(−1, 6\right)$. Find the exact equation of the function.

Write an equation using the given roots.

$y = a\left(x + 2\right)^{2} \left(x − 2\right)$

Substitute the given point to find the value of a.

$y = −2\left(x + 2\right)^{2}\left(x − 2\right)$