Answer
$y=\dfrac{1}{3}(x-2)(x-7)$
Work Step by Step
Here, we find the x-intercepts are $2$ and $7$.
Thus, the function is: $y=a (x-2)(x-7)$
Since $(4,-2)$ is on the graph of this function, we have
$-2=a (x-2)(x-7)$
This gives: $-2=-6a \implies a=\dfrac{1}{3}$
Hence, the required function is:
$y=\dfrac{1}{3}(x-2)(x-7)$