# How do you write the equation of the quadratic function with roots 0 and 1 and a vertex at (-1/2, 2)?

The function is: $y = \frac{8}{3} {x}^{2} - \frac{8}{3} x$.
Assuming you are looking for a function $f \left(x\right) = a {x}^{2} + b x + c$, you can find the equation by solving the following sysyem of equations:
$\left\{\begin{matrix}f \left(0\right) = 0 \\ f \left(1\right) = 0 \\ f \left(- \frac{1}{2}\right) = 2\end{matrix}\right.$
$\left\{\begin{matrix}c = 0 \\ a + b = 0 \\ \frac{1}{4} a - \frac{1}{2} b = 0\end{matrix}\right.$