y= 2x^2 + 16x + 33
You asked:
Investigate the equation: \(y = 2 \cdot {x}^{2} + 16 x + 33\).
MathBot Answer:
The graph of the equation \(y = 2 \cdot {x}^{2} + 16 x + 33\) is a parabola.
The coordinates of its vertex are: \(\left(-4, 1\right)\)
The coordinates of its focus are: \(\left(-4, \frac{9}{8}\right)\)
The directrix has equation: \(8 y - 7 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= -4 + \theta\\y\left(\theta\right) &= 1 + 2 \theta^{2}\end{aligned}\]