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Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the parabola in vertex form.

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We have been given that a parabola has vertex
(-8,-7) and also passes through the point
(-7,-4). We are asked to write the equation of the parabola in vertex form.

We know that vertex form of parabola in format
y=a(x-h)^2+k, with a vertex at point (h,k).

Let us write equation of parabola using our given information as:


y=a(x-(-8))^2-7


y=a(x+8)^2-7

Now we will substitute the coordinates of point
(-7,-4) to solve for a as:


-4=a(-7+8)^2-7


-4=a(1)^2-7


-4+7=a-7+7


3=a

Therefore, our required equation would be
y=3(x+8)^2-7.

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