Question

12. (24.4D) For what value of c will the graphs of

y = 2x2 - 36x + c and y = 2(x - 9)2 - 18
be the same?

Answer 1

`c=144`

Explanation:

we have

`y=2x^2-36x+c` ---> equation A

`y=2(x-9)^2-18` ---> equation B

Convert the equation A into vertex form and then compare with equation B

we have

`y=2x^2-36x+c`

Factor 2 leading coefficient

`y=2(x^2-18x)+c`

Complete the square

`y=2(x^2-18x+81)+c-162`

Rewrite as perfect squares

`y=2(x-9)^2+(c-162)`

Compare with equation B

`c-162=-18`

solve for c

`c=-18+162`

`c=144`