x^2+4x-s=0
You asked:
Investigate the equation: \({x}^{2} + 4 x - s = 0\).
MathBot Answer:
The graph of the equation \({x}^{2} + 4 x - s = 0\) is a parabola.
The coordinates of its vertex are: \(\left(-4, -2\right)\)
The coordinates of its focus are: \(\left(- \frac{15}{4}, -2\right)\)
The directrix has equation: \(4 s + 17 = 0\).
The parabola has parameterization: \[\begin{aligned}s\left(\theta\right) &= -4 + \theta^{2}\\x\left(\theta\right) &= -2 + \theta\end{aligned}\]