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

Answer:

$c=144$

Step-by-step 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

$c=-18+162$

$c=144$