Answer
$y=-\frac{5}{4}(x-2)^{2}+7$
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 $a$...
$y=a(x-h)^{2}+k$
$2=a(4-2)^{2}+7$
$-5=a(2)^{2}$
$-5=4a$
$a=-\frac{5}{4}$
Therefore the function is...
$y=-\frac{5}{4}(x-2)^{2}+7$
