Answer
$y=-\frac{1}{2}(x+3)^{2}-2$
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 $a$...
$y=a(x-h)^{2}+k$
$-10=a(1+3)^{2}-2$
$-8=a(4)^{2}$
$-8=16a$
$a=-\frac{8}{16}$
$a=-\frac{1}{2}$
Therefore the function is...
$y=-\frac{1}{2}(x+3)^{2}-2$
