y=x^2-x/2-3
You asked:
Investigate the equation: \(y = {x}^{2} - \frac{x}{2} - 3\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} - \frac{x}{2} - 3\) is a parabola.
The coordinates of its vertex are: \(\left(\frac{1}{4}, - \frac{49}{16}\right)\)
The coordinates of its focus are: \(\left(\frac{1}{4}, - \frac{45}{16}\right)\)
The directrix has equation: \(4 y + \frac{53}{4} = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \frac{1}{4} + \theta\\y\left(\theta\right) &= - \frac{49}{16} + \theta^{2}\end{aligned}\]