y=(x-2)^2-4
You asked:
Investigate the equation: \(y = {\left( x - 2 \right)}^{2} - 4\).
MathBot Answer:
The graph of the equation \(y = {\left( x - 2 \right)}^{2} - 4\) is a parabola.
The coordinates of its vertex are: \(\left(2, -4\right)\)
The coordinates of its focus are: \(\left(2, - \frac{15}{4}\right)\)
The directrix has equation: \(4 y + 17 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= 2 + \theta\\y\left(\theta\right) &= -4 + \theta^{2}\end{aligned}\]