Answer:
[tex]c=144[/tex]
Step-by-step explanation:
we have
[tex]y=2x^2-36x+c[/tex] ---> equation A
[tex]y=2(x-9)^2-18[/tex] ---> equation B
Convert the equation A into vertex form and then compare with equation B
we have
[tex]y=2x^2-36x+c[/tex]
Factor 2 leading coefficient
[tex]y=2(x^2-18x)+c[/tex]
Complete the square
[tex]y=2(x^2-18x+81)+c-162[/tex]
Rewrite as perfect squares
[tex]y=2(x-9)^2+(c-162)[/tex]
Compare with equation B
[tex]c-162=-18[/tex]
solve for c
[tex]c=-18+162[/tex]
[tex]c=144[/tex]
