vertex

We can simplifify this equation first. 

 

x - y^2 + 8y = 13 + 2y + y^2 - 7y - 14

x+8y=13+2y+2y^2 -7y-14

x+8y=2y+2y^2 -7y -1

x+6y=2y^2 - 7y - 1

x+13y=2y^2-2

x=2y^2-13y-1

 

Then we can write this into vertex form, try this part yourself! 

 

If needed, help for this step can be found through MathWay.

 

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Here it is! (13/4, -177/8)