x^2-2x-4 = y
You asked:
Investigate the equation: \({x}^{2} - 2 x - 4 = y\).
MathBot Answer:
The graph of the equation \({x}^{2} - 2 x - 4 = y\) is a parabola.
The coordinates of its vertex are: \(\left(1, -5\right)\)
The coordinates of its focus are: \(\left(1, - \frac{19}{4}\right)\)
The directrix has equation: \(4 y + 21 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= 1 + \theta\\y\left(\theta\right) &= -5 + \theta^{2}\end{aligned}\]