Answer
$y=\frac{19}{81}(x-\frac{5}{2})^2-\frac{3}{4}$
Work Step by Step
Vertex: $(h,k)=(\frac{5}{2},-\frac{3}{4})$
Standard form:
$y=a(x−h)^2+k$
$y=a(x-\frac{5}{2})^2-\frac{3}{4}$
Now, use the point $(−2,4)$ to find $a$:
$4=a(-2-\frac{5}{2})^2-\frac{3}{4}$
$4+\frac{3}{4}=a(-\frac{9}{2})^2$
$\frac{19}{4}=a(\frac{81}{4})$
$a=\frac{\frac{19}{4}}{\frac{81}{4}}=\frac{19}{4}\frac{4}{81}=\frac{19}{81}$
$y=\frac{19}{81}(x-\frac{5}{2})^2-\frac{3}{4}$
