Question 974252

{{{Y=x^2-9x+20}}}
{{{Y=(x^2-9x)+20}}}......complete square
{{{Y=(x^2-9x+b^2)-b^2+20}}}...compare to {{{(a-b)^2=a^2-2ab+b^2}}};as you can see, {{{a=1}}} and {{{2ab=9}}}
=>{{{2*1*b=9}}}=>{{{2b=9}}}=>{{{b=9/2}}}, then we have
{{{Y=(x^2-9x+(9/2)^2)-(9/2)^2+20}}}
{{{Y=(x-9/2)^2-81/4+20}}}
{{{Y=(x-9/2)^2-81/4+80/4}}}
{{{Y=(x-9/2)^2-1/4}}}
=> {{{h=9/2}}} and {{{k=-1/4}}}



{{{Y=x^2-7x-8}}}

{{{Y=(x^2-7x)-8}}}

{{{Y=(x^2-7x+b^2)-b^2-8}}}...=>{{{a=1}}} and{{{2ab=7}}}=>{{{2*1*b=7}}}=>{{{2b=7}}}=>{{{b=7/2}}}, then we have

{{{Y=(x^2-7x+(7/2)^2)-(7/2)^2-8}}}

{{{Y=(x-7/2)^2-49/4-8}}}

{{{Y=(x-7/2)^2-49/4-32/4}}}

{{{Y=(x-7/2)^2-81/4}}}



{{{Y=x^2+4x-9}}}

{{{Y=(x^2+4x)-9}}}

{{{Y=(x^2+4x+b^2)-b^2-9}}}...=>{{{a=1}}} and{{{2ab=4}}}=>{{{2*1*b=4}}}=>{{{2b=4}}}=>{{{b=2}}}, then we have

{{{Y=(x^2+4x+2^2)-2^2-9}}}

{{{Y=(x+2)^2-4-9}}}

{{{Y=(x+2)^2-13}}}