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