Answer
See below
Work Step by Step
We already know $y$, $x$, $k$ and $h$ from the given vertex and point, so in order to get the quadratic function we need to find $a$.
$y=a(x-h)(x-k)$
$-40=a(7+3)(7-5)$
$-40=20a$
$a=-2$
Therefore the function is:
$y=-2(x+3)(x-5)$