s-8=\frac{t^2+8s}{20}
You asked:
Investigate the equation: \(s - 8 = \frac{{t}^{2} + 8 s}{20}\).
MathBot Answer:
The graph of the equation \(s - 8 = \frac{{t}^{2} + 8 s}{20}\) is a parabola.
The coordinates of its vertex are: \(\left(\frac{40}{3}, 0\right)\)
The coordinates of its focus are: \(\left(\frac{49}{3}, 0\right)\)
The directrix has equation: \(\frac{s}{3} - \frac{31}{9} = 0\).
The parabola has parameterization: \[\begin{aligned}s\left(\theta\right) &= \frac{40}{3} + \frac{\theta^{2}}{12}\\t\left(\theta\right) &= \theta\end{aligned}\]