y=1-x^{2}
You asked:
Investigate the equation: \(y = 1 - {x}^{2}\).
MathBot Answer:
The graph of the equation \(y = 1 - {x}^{2}\) 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: \[\begin{aligned}x\left(\theta\right) &= \theta\\y\left(\theta\right) &= 1 - \theta^{2}\end{aligned}\]