y = $x^{2}$ + 8x + 19
You asked:
Investigate the equation: \(y = {x}^{2} + 8 x + 19\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} + 8 x + 19\) is a parabola.
The coordinates of its vertex are: \(\left(-4, 3\right)\)
The coordinates of its focus are: \(\left(-4, \frac{13}{4}\right)\)
The directrix has equation: \(4 y - 11 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= -4 + \theta\\y\left(\theta\right) &= 3 + \theta^{2}\end{aligned}\]