X²+6x+4=0
You asked:
Investigate the equation: \({X}^{2} + 6 x + 4 = 0\).
MathBot Answer:
The graph of the equation \({X}^{2} + 6 x + 4 = 0\) is a parabola.
The coordinates of its vertex are: \(\left(0, - \frac{2}{3}\right)\)
The coordinates of its focus are: \(\left(0, - \frac{13}{6}\right)\)
The directrix has equation: \(- \frac{2 x}{3} + \frac{5}{9} = 0\).
The parabola has parameterization: \[\begin{aligned}X\left(\theta\right) &= \theta\\x\left(\theta\right) &= - \frac{2}{3} - \frac{\theta^{2}}{6}\end{aligned}\]