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