y = x**2 + x*2 + 16
You asked:
Investigate the equation: \(y = {x}^{2} + x \cdot 2 + 16\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} + x \cdot 2 + 16\) is a parabola.
The coordinates of its vertex are: \(\left(-1, 15\right)\)
The coordinates of its focus are: \(\left(-1, \frac{61}{4}\right)\)
The directrix has equation: \(4 y - 59 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= -1 + \theta\\y\left(\theta\right) &= 15 + \theta^{2}\end{aligned}\]