Answer
$y=\frac{3}{4}(x-2)^2-\frac{5}{2}$
Work Step by Step
Vertex: $(h,k)=(2,-\frac{5}{2})$
Standard form:
$y=a(x-h)^2+k$
$y=a(x-2)^2+(-\frac{5}{2})$
$y=a(x-2)^2-\frac{5}{2}$
Now, use the point $(4,\frac{1}{2})$ to find $a$:
$\frac{1}{2}=a(4-2)^2-\frac{5}{2}$
$\frac{1}{2}+\frac{5}{2}=a(4)$
$a=\frac{3}{4}$
$y=\frac{3}{4}(x-2)^2-\frac{5}{2}$
