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What is the equation for a parabola with a vertex of (5,-2) and a point (6,1)?   ...

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What is the equation for a parabola with a vertex of (5,-2) and a point (6,1)?   

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To determine the equation, use the vertex form of the parabola which is:

`y=a(x-h)^2+k`

Plug-in the given vertex (5,-2).

`y=a(x-5)^2+(-2)`

`y=a(x-5)^2-2`

To get the value of a, plug-in the point (6,1).

`1=a(6-5)^2-2`

`1=a(1)^2-2`

`1=a-2`

`1+2=a-2+2`

`3=a`

Hence, the equation of the parabola is `y=3(x-5)^2-2` .

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