y= x^2 - 2x + 3
You asked:
Investigate the equation: \(y = {x}^{2} - 2 x + 3\).
MathBot Answer:
The graph of the equation \(y = {x}^{2} - 2 x + 3\) is a parabola.
The coordinates of its vertex are: \(\left(1, 2\right)\)
The coordinates of its focus are: \(\left(1, \frac{9}{4}\right)\)
The directrix has equation: \(4 y - 7 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= 1 + \theta\\y\left(\theta\right) &= 2 + \theta^{2}\end{aligned}\]