y=x^2-1
You asked:
Investigate the equation: \(y = {x}^{2} - 1\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} - 1\) is a parabola.
The coordinates of its vertex are: \(\left(0, -1\right)\)
The coordinates of its focus are: \(\left(0, - \frac{3}{4}\right)\)
The directrix has equation: \(4 y + 5 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \theta\\y\left(\theta\right) &= -1 + \theta^{2}\end{aligned}\]