y=-(x-3)²+5

asked by guest
on Mar 16, 2025 at 7:04 pm



You asked:

Investigate the equation: y=(x3)2+5y = -{\left( x - 3 \right)}^{2} + 5.

MathBot Answer:

The graph of the equation y=(x3)2+5y = -{\left( x - 3 \right)}^{2} + 5 is a parabola.


The coordinates of its vertex are: (3,5)\left(3, 5\right)

The coordinates of its focus are: (3,194)\left(3, \frac{19}{4}\right)

The directrix has equation: 4y+21=0- 4 y + 21 = 0.

The parabola has parameterization: x(θ)=3+θy(θ)=5θ2\begin{aligned}x\left(\theta\right) &= 3 + \theta\\y\left(\theta\right) &= 5 - \theta^{2}\end{aligned}

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