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Find the vertex of the graph of the equation x - y^2 + 8y = 13. 

 Jul 18, 2023
 #1
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We can rewrite the equation as [y^2 - 8y + (x - 13) = 0.]Completing the square, we get [(y - 4)^2 - 16 + (x - 13) = 0.]Then [(y - 4)^2 = x - 7,]so y=4±x−7​.

The vertex is the point where the parabola changes concavity, so it is the point where the discriminant of the quadratic is 0. This occurs when x−7=0, so the vertex is (7,4)​.

 Jul 18, 2023
 #2
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This is correct.

 

GA

Guest Jul 18, 2023
 #3
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hey...you know you cold just use desmos for that problem...

https://www.desmos.com/calculator

 Jul 19, 2023
 #4
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and btw,...the vertex is    (-3,4)

 Jul 19, 2023

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