y=x²+9x+15
You asked:
Investigate the equation: \(y = {x}^{2} + 9 x + 15\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} + 9 x + 15\) is a parabola.
The coordinates of its vertex are: \(\left(- \frac{9}{2}, - \frac{21}{4}\right)\)
The coordinates of its focus are: \(\left(- \frac{9}{2}, -5\right)\)
The directrix has equation: \(4 y + 22 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= - \frac{9}{2} + \theta\\y\left(\theta\right) &= - \frac{21}{4} + \theta^{2}\end{aligned}\]