y= $x^{2}$ -5
You asked:
Investigate the equation: \(y = {x}^{2} - 5\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} - 5\) is a parabola.
The coordinates of its vertex are: \(\left(0, -5\right)\)
The coordinates of its focus are: \(\left(0, - \frac{19}{4}\right)\)
The directrix has equation: \(4 y + 21 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \theta\\y\left(\theta\right) &= -5 + \theta^{2}\end{aligned}\]