y= $3x^{2}$+2x+10
You asked:
Investigate the equation: \(y = 3 {x}^{2} + 2 x + 10\).
MathBot Answer:
The graph of the equation \(y = 3 {x}^{2} + 2 x + 10\) is a parabola.
The coordinates of its vertex are: \(\left(- \frac{1}{3}, \frac{29}{3}\right)\)
The coordinates of its focus are: \(\left(- \frac{1}{3}, \frac{39}{4}\right)\)
The directrix has equation: \(12 y - 115 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= - \frac{1}{3} + \theta\\y\left(\theta\right) &= \frac{29}{3} + 3 \theta^{2}\end{aligned}\]