Answer
$y=-\frac{24}{49}(x+\frac{1}{4})^2+\frac{3}{2}$
Work Step by Step
Vertex: $(h,k)=(-\frac{1}{4},\frac{3}{2})$
Standard form:
$y=a(x−h)^2+k$
$y=a[x-(-\frac{1}{4})]^2+\frac{3}{2}$
$y=a(x+\frac{1}{4})^2+\frac{3}{2}$
Now, use the point $(−2,0)$ to find $a$:
$0=a(-2+\frac{1}{4})^2+\frac{3}{2}$
$-\frac{3}{2}=a(-\frac{7}{4})^2=a(\frac{49}{16})$
$a=\frac{-\frac{3}{2}}{\frac{49}{16}}=-\frac{3}{2}\frac{16}{49}=-\frac{24}{49}$
$y=-\frac{24}{49}(x+\frac{1}{4})^2+\frac{3}{2}$
