y=3x^2-18x+25
You asked:
Investigate the equation: \(y = 3 \cdot {x}^{2} - 18 x + 25\).
MathBot Answer:
The graph of the equation \(y = 3 \cdot {x}^{2} - 18 x + 25\) is a parabola.
The coordinates of its vertex are: \(\left(3, -2\right)\)
The coordinates of its focus are: \(\left(3, - \frac{23}{12}\right)\)
The directrix has equation: \(12 y + 25 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= 3 + \theta\\y\left(\theta\right) &= -2 + 3 \theta^{2}\end{aligned}\]