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Find the vertex of the graph of the equation \( x - y^2 + 8y = 13\)

 Feb 11, 2021
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x  - y^2  +  8y  =   13

 

Rearrange  as

 

x =  y^2  -  8y  +  13         complete the  square on y

 

take (1/2)  of 8  =4.....square it  = 16      add  and  subtract on the right side

 

x  =  y^2  -  8y  +  16 +  13  -16           factor  and simplify

 

x =  (y - 4)^2    -  3       add 3 to both sides

 

(x + 3)  = ( y -4)^2

 

We have  the  form     ( x - h)  =  ( y - k)^2     where  the  vertex  =  ( h , k)

 

So  the  vertex  is  ( -3, 4)

 

See the graph here : https://www.desmos.com/calculator/6pqzy8femz

 

 

 

cool cool cool

 Feb 11, 2021

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