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