Answer
$y=x(x+3)$
Work Step by Step
We already know $y$, $x$, $p$ and $q$ from the given x-intercepts and the point, so in order to get the quadratic function we need to find $a$...
$y=a(x-p)(x-q)$
$10=a(2+3)a(0+2)$
$10=10a$
$a=\frac{10}{10}$
$a=1$
Therefore the functions is...
$y=x(x+3)$