y = x² + 5x + 3
You asked:
Investigate the equation: \(y = {x}^{2} + 5 x + 3\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} + 5 x + 3\) is a parabola.
The coordinates of its vertex are: \(\left(- \frac{5}{2}, - \frac{13}{4}\right)\)
The coordinates of its focus are: \(\left(- \frac{5}{2}, -3\right)\)
The directrix has equation: \(4 y + 14 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= - \frac{5}{2} + \theta\\y\left(\theta\right) &= - \frac{13}{4} + \theta^{2}\end{aligned}\]