y= 2x^2 +4x
You asked:
Investigate the equation: \(y = 2 {x}^{2} + 4 x\).
MathBot Answer:
The graph of the equation \(y = 2 {x}^{2} + 4 x\) is a parabola.
The coordinates of its vertex are: \(\left(-1, -2\right)\)
The coordinates of its focus are: \(\left(-1, - \frac{15}{8}\right)\)
The directrix has equation: \(8 y + 17 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= -1 + \theta\\y\left(\theta\right) &= -2 + 2 \theta^{2}\end{aligned}\]