write as:
y=3/7x^2+2/7x-4/7..................................(1)
y=3/7(x^2+color(blue)(2/3x))-4/7
consider the 2/3" from "color(blue)( 2/3x)" and multiply it by "color(brown)( 1/2)
color(brown)(1/2)xxcolor(blue)(2/3)=color(green)(1/3)
y!=3/7(x+color(green)(1/3))^2-4/7" "color(purple)(" This introduces an error!")
Let k be some constant then:
y=3/7(x+1/3)^2+k-4/7 ...................(2) color(purple)("Corrected the error!")
expanding to find the value of k
y=3/7x^2+2/7x+1/21+k-4/7 ......................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Equate equation (1) to equation (3) through y
cancel(3/7x^2)+cancel(2/7x)-cancel(4/7)" "=" "cancel(3/7x^2)+cancel(2/7x)+1/21+k-cancel(4/7)
k+1/21=0" "->" "k=-1/21.............................(4)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute (4) into (2) giving
y=3/7(x+1/3)^2-1/21-4/7 ...................(2_a)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solution:
y=3/7(x+1/3)^2-13/21
color(purple)("Please check the arithmetic. I can not spot any error but I am not") color(purple)("totally satisfied with the answer!")
