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Translate the following conic from standard form to graphing form

x ^ 2 + 2x + u ^ 2 - 8y + 1 = 0

User Victtim
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Answer:

To convert the given conic equation from standard form to graphing form (also known as the vertex form), we need to complete the square for both x and y terms.

Given equation: x^2 + 2x + u^2 - 8y + 1 = 0

First, let's complete the square for the x terms:

x^2 + 2x can be rewritten as (x + 1)^2 - 1, since (x + 1)^2 expands to x^2 + 2x + 1.

Now we need to complete the square for the y terms:

Since we only have -8y, let's rewrite it as -8(y - 1), so that we have a perfect square in y.

Substitute the transformed x and y terms back into the equation:

(x + 1)^2 - 1 + u^2 - 8(y - 1) + 1 = 0

Simplify the equation:

(x + 1)^2 + u^2 - 8(y - 1) = 0

Now, we have the conic equation in graphing (vertex) form:

(x + 1)^2 + u^2 - 8(y - 1) = 0

User Stenlytw
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