Math Problem Solver

The graph of the equation $y = -{\left( x - 3 \right)}^{2} + 5$ is a parabola.

The coordinates of its vertex are: $\left(3, 5\right)$

The coordinates of its focus are: $\left(3, \frac{19}{4}\right)$

The directrix has equation: $- 4 y + 21 = 0$.

The parabola has parameterization: $$\begin{aligned}x\left(\theta\right) &= 3 + \theta\\y\left(\theta\right) &= 5 - \theta^{2}\end{aligned}$$