How do you write #y=9x^2+3x-10# in vertex form?

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Answer 1 · 2014-11-17T23:27:00

Recall

#x^2+2ax+a^2=(x-a)^2#

#y=9x^2+3x-10#

by factoring 9 out of the first two terms,

#=9(x^2+1/3x)-10#

since #2a=1/3 => a=1/6 => a^2=1/36#, by adding and subtracting #1/36#,

#=9(x^2+1/3x+1/36-1/36)-10#

by keeping the first three term in the parentheses,

#=9(x^2+1/3x+1/36)-9/36-10#

#=9(x+1/6)^2-41/4#

I hope that this was helpful.