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