y=(1/2)(x+1)²-3

asked by guest
on Mar 16, 2025 at 7:07 pm



You asked:

Investigate the equation: y=12(x+1)23y = \frac{1}{2} {\left( x + 1 \right)}^{2} - 3.

MathBot Answer:

The graph of the equation y=12(x+1)23y = \frac{1}{2} {\left( x + 1 \right)}^{2} - 3 is a parabola.


The coordinates of its vertex are: (1,3)\left(-1, -3\right)

The coordinates of its focus are: (1,52)\left(-1, - \frac{5}{2}\right)

The directrix has equation: 2y+7=02 y + 7 = 0.

The parabola has parameterization: x(θ)=1+θy(θ)=3+θ22\begin{aligned}x\left(\theta\right) &= -1 + \theta\\y\left(\theta\right) &= -3 + \frac{\theta^{2}}{2}\end{aligned}

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