y= -2x^2 - 4x - 3
You asked:
Investigate the equation: \(y = -\left( 2 \cdot {x}^{2} \right) - 4 x - 3\).
MathBot Answer:
The graph of the equation \(y = -\left( 2 \cdot {x}^{2} \right) - 4 x - 3\) is a parabola.
The coordinates of its vertex are: \(\left(-1, -1\right)\)
The coordinates of its focus are: \(\left(-1, - \frac{9}{8}\right)\)
The directrix has equation: \(- 8 y - 7 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= -1 + \theta\\y\left(\theta\right) &= -1 - 2 \theta^{2}\end{aligned}\]