Answer
$y=-\frac{7}{8}(x+\frac{1}{4})^2+7$
Work Step by Step
Vertex: $(h,k)=(-\frac{1}{4},7)$
Standard form:
$y=a(x-h)^2+k$
$y=a[x-(-\frac{1}{4})]^2+7$
$y=a(x+\frac{1}{4})^2+7$
Now, use the point $(\frac{3}{4},\frac{49}{8})$ to find $a$:
$\frac{49}{8}=a(\frac{3}{4}+\frac{1}{4})^2+7$
$\frac{49}{8}-7=a(1)^2$
$a=-\frac{7}{8}$
$y=-\frac{7}{8}(x+\frac{1}{4})^2+7$
