$\frac{y-10}{3}$=$x^{2}$+2x
You asked:
Investigate the equation: \(\frac{y - 10}{3} = {x}^{2} + 2 x\).
MathBot Answer:
The graph of the equation \(\frac{y - 10}{3} = {x}^{2} + 2 x\) is a parabola.
The coordinates of its vertex are: \(\left(-1, 7\right)\)
The coordinates of its focus are: \(\left(-1, \frac{85}{12}\right)\)
The directrix has equation: \(12 y - 83 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= -1 + \theta\\y\left(\theta\right) &= 7 + 3 \theta^{2}\end{aligned}\]