Third-degree means that the highest power of $x$ will be $3$.

The roots are $3, 2$, and $−1$. These three values make the polynomial equal to $0$.

The corresponding polynomial is $y = a\left(x − 3\right)\left(x − 2\right)\left(x + 1\right)$.

Substitute the point $\left(1, 1\right)$ into the polynomial equation to find the value of $a$.

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