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