y=-3x^{2}+6x+9
You asked:
Investigate the equation: \(y = -\left( 3 {x}^{2} \right) + 6 x + 9\).
MathBot Answer:
The graph of the equation \(y = -\left( 3 {x}^{2} \right) + 6 x + 9\) is a parabola.
The coordinates of its vertex are: \(\left(1, 12\right)\)
The coordinates of its focus are: \(\left(1, \frac{143}{12}\right)\)
The directrix has equation: \(- 12 y + 145 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= 1 + \theta\\y\left(\theta\right) &= 12 - 3 \theta^{2}\end{aligned}\]