y = x^{2} - x + 8
You asked:
Investigate the equation: \(y = {x}^{2} - x + 8\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} - x + 8\) is a parabola.
The coordinates of its vertex are: \(\left(\frac{1}{2}, \frac{31}{4}\right)\)
The coordinates of its focus are: \(\left(\frac{1}{2}, 8\right)\)
The directrix has equation: \(4 y - 30 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \frac{1}{2} + \theta\\y\left(\theta\right) &= \frac{31}{4} + \theta^{2}\end{aligned}\]