Answer
$y=\frac{3}{4}(x-5)^2+12$
Work Step by Step
Vertex: $(h,k)=(5,12)$
Standard form:
$y=a(x-h)^2+k$
$y=a(x-5)^2+12$
Now, use the point $(7,15)$ to find $a$:
$15=a(7-5)^2+12$
$15-12=a(4)$
$a=\frac{3}{4}$
$y=\frac{3}{4}(x-5)^2+12$