Math Problem Solver

The graph of the equation $y = {x}^{2} - x$ is a parabola.

The coordinates of its vertex are: $\left(\frac{1}{2}, - \frac{1}{4}\right)$

The coordinates of its focus are: $\left(\frac{1}{2}, 0\right)$

The directrix has equation: $4 y + 2 = 0$.

The parabola has parameterization: $$\begin{aligned}x\left(\theta\right) &= \frac{1}{2} + \theta\\y\left(\theta\right) &= - \frac{1}{4} + \theta^{2}\end{aligned}$$