Chapter 3 - Quadratic Functions - 3.2 The Vertex of a Parabola - Exercises and Problems for Section 3.2 - Exercises and Problems - Page 128: 34

$ y=12\cdot\left(x-\frac{1}{2}\right)^2 $

We have $y=a(x-1 / 2)^2$. Since $(0,3)$ is on the curve, Solve for $a$ $$ \begin{aligned} a(-1/2)^2 & =3 \\ 1/4a & =3 \\ a & =12 \end{aligned} $$ Hence $$ y=12\cdot\left(x-\frac{1}{2}\right)^2 $$