$3x^{2}$ +2y=7
You asked:
Investigate the equation: \(3 \cdot {x}^{2} + 2 y = 7\).
MathBot Answer:
The graph of the equation \(3 \cdot {x}^{2} + 2 y = 7\) is a parabola.
The coordinates of its vertex are: \(\left(0, \frac{7}{2}\right)\)
The coordinates of its focus are: \(\left(0, \frac{10}{3}\right)\)
The directrix has equation: \(- 6 y + 22 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \theta\\y\left(\theta\right) &= \frac{7}{2} - \frac{3 \theta^{2}}{2}\end{aligned}\]