y=-x(x-3)
You asked:
Investigate the equation: \(y = -x\left( x - 3 \right)\).
MathBot Answer:
The graph of the equation \(y = -\left( x \cdot \left(x - 3\right) \right)\) is a parabola.
The coordinates of its vertex are: \(\left(\frac{3}{2}, \frac{9}{4}\right)\)
The coordinates of its focus are: \(\left(\frac{3}{2}, 2\right)\)
The directrix has equation: \(- 4 y + 10 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \frac{3}{2} + \theta\\y\left(\theta\right) &= \frac{9}{4} - \theta^{2}\end{aligned}\]