What is the vertex form of #y= 9x^2 + 2x + 2/7 #?

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Answer 1 · 2018-02-26T01:59:10

See below:

#y=a(x-h)^2+k# with #(h,k)# as the vertex.

To find the vertex form of a quadratic equation, complete the square:

#y=9(x^2+2/9x+(1/9)^2-(1/9)^2)+2/7#

#y=9(x+1/9)^2-9/81+2/7#

#y=9(x+1/9)^2+11/63#

The vertex is #(-1/9,11/63)#

You can also find the vertex with formulas:

#h=-b/(2a)#

#k=c-b^2/(4a)#

#------------#

#h=-2/(2*9)=-1/9#

#k=2/7-(-2)^2/(4*9)=2/7-4/36=11/63#

so the vertex is at

#(-1/9,11/63)#

You can also find vertex form this way:

#y=a(x+1/9)+11/63#

Plug in #a# from the original equation:

#y=9(x+1/9)+11/63#

Apologies for the length :)