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

1 Answer
Nov 17, 2014

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

by completing the square,

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


I hope that this was helpful.