Question 118946
To find the axis of symmetry, take the x coefficient {{{-6b}}} and divide it by {{{2*2}}} and negate it. Remember, for {{{y=2x^2 - 6bx+3}}}, the axis of symmetry is {{{x=-b/2a}}}. So in our case,  {{{x=-(-6b)/(2*2)}}}. Since the axis of symmetry is x=9, this means 



{{{9=-(-6b)/(2*2)}}} Plug in x=9



{{{9=6b/(2*2)}}} Negate -6b



{{{9=6b/4}}} Multiply




{{{36=6b}}} Multiply both sides by 4



{{{6=b}}} Divide both sides by 6



So our answer is {{{b=6}}}. So you are correct.


If we plug in {{{b=6}}} into {{{y=2x^2 - 6bx+3}}}, we get


{{{y=2x^2 - 6(6)x+3}}} Plug in b=6




{{{y=2x^2 - 36x+3}}} Multiply



Now let's graph



{{{ graph( 500, 500, -30, 30, -160, 10, 2x^2 - 36x+3) }}}



So we can see that the axis of symmetry is x=9. So this verifies our answer.