Math Problem Solver

The graph of the equation $y = \frac{1}{2} {\left( x + 1 \right)}^{2} - 3$ is a parabola.

The coordinates of its vertex are: $\left(-1, -3\right)$

The coordinates of its focus are: $\left(-1, - \frac{5}{2}\right)$

The directrix has equation: $2 y + 7 = 0$.

The parabola has parameterization: $$\begin{aligned}x\left(\theta\right) &= -1 + \theta\\y\left(\theta\right) &= -3 + \frac{\theta^{2}}{2}\end{aligned}$$