y=(x-4)(x-2)
You asked:
Investigate the equation: \(y = \left(x - 4\right) \cdot \left(x - 2\right)\).
MathBot Answer:
The graph of the equation \(y = \left(x - 4\right) \cdot \left(x - 2\right)\) is a parabola.
The coordinates of its vertex are: \(\left(3, -1\right)\)
The coordinates of its focus are: \(\left(3, - \frac{3}{4}\right)\)
The directrix has equation: \(4 y + 5 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= 3 + \theta\\y\left(\theta\right) &= -1 + \theta^{2}\end{aligned}\]