solve x^2 + 13x + 23 = y
You asked:
Investigate the equation: \({x}^{2} + 13 x + 23 = y\).
MathBot Answer:
The graph of the equation \({x}^{2} + 13 x + 23 = y\) is a parabola.
The coordinates of its vertex are: \(\left(- \frac{13}{2}, - \frac{77}{4}\right)\)
The coordinates of its focus are: \(\left(- \frac{13}{2}, -19\right)\)
The directrix has equation: \(4 y + 78 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= - \frac{13}{2} + \theta\\y\left(\theta\right) &= - \frac{77}{4} + \theta^{2}\end{aligned}\]