What is the equation of a parabola with a vertex of (5,-2) and point of (6,1)?
Include "y=" as part of your answer.
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The equation of a parabola in vertex form is `y=a(x-h)^2+k` where (h,k) is the vertex.
Here, vertex is (5,-2)
We also have a point (x,y) = (6,1). So let's plug these in and find 'a'.
Here a is positive so the parabola opens upwards like a regular "U".
Now, rewrite the equation `y=a(x-h)^2+k`
Substituting a=3, h=5 and k=-2 we get:
Therefore, the equation of the parabola is `y=3x^2-30x+73`
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