64x^2 -8=y
You asked:
Investigate the equation: \(64 \cdot {x}^{2} - 8 = y\).
MathBot Answer:
The graph of the equation \(64 \cdot {x}^{2} - 8 = y\) is a parabola.
The coordinates of its vertex are: \(\left(0, -8\right)\)
The coordinates of its focus are: \(\left(0, - \frac{2047}{256}\right)\)
The directrix has equation: \(256 y + 2049 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \theta\\y\left(\theta\right) &= -8 + 64 \theta^{2}\end{aligned}\]