y = x ^ 2 + 4x - 5
You asked:
Investigate the equation: \(y = {x}^{2} + 4 x - 5\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} + 4 x - 5\) is a parabola.
The coordinates of its vertex are: \(\left(-2, -9\right)\)
The coordinates of its focus are: \(\left(-2, - \frac{35}{4}\right)\)
The directrix has equation: \(4 y + 37 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= -2 + \theta\\y\left(\theta\right) &= -9 + \theta^{2}\end{aligned}\]