y= -x^2+4
You asked:
Investigate the equation: \(y = -{x}^{2} + 4\).
MathBot Answer:
The graph of the equation \(y = -{x}^{2} + 4\) is a parabola.
The coordinates of its vertex are: \(\left(0, 4\right)\)
The coordinates of its focus are: \(\left(0, \frac{15}{4}\right)\)
The directrix has equation: \(- 4 y + 17 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \theta\\y\left(\theta\right) &= 4 - \theta^{2}\end{aligned}\]