y=2x^2-6x-20
You asked:
Investigate the equation: \(y = 2 \cdot {x}^{2} - 6 x - 20\).
MathBot Answer:
The graph of the equation \(y = 2 \cdot {x}^{2} - 6 x - 20\) is a parabola.
The coordinates of its vertex are: \(\left(\frac{3}{2}, - \frac{49}{2}\right)\)
The coordinates of its focus are: \(\left(\frac{3}{2}, - \frac{195}{8}\right)\)
The directrix has equation: \(8 y + 197 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \frac{3}{2} + \theta\\y\left(\theta\right) &= - \frac{49}{2} + 2 \theta^{2}\end{aligned}\]