Math Problem Solver

The graph of the equation $y = -{x}^{2} + x + 5.75$ is a parabola.

The coordinates of its vertex are: $\left(\frac{1}{2}, 6\right)$

The coordinates of its focus are: $\left(\frac{1}{2}, \frac{23}{4}\right)$

The directrix has equation: $- 4 y + 25 = 0$.

The parabola has parameterization: $$\begin{aligned}x\left(\theta\right) &= \frac{1}{2} + \theta\\y\left(\theta\right) &= 6 - \theta^{2}\end{aligned}$$