Question

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

y=3(x-7/2)^2-27/4
y=2(x-1)^2-11
y=2(x-1/2)^2-53/4
y=2(x-1/2)^2-27/2

Answer 1

y= 3( x -2 )² - ( x-5 )² = 3 ( x² - 4 x + 4 ) - ( x² - 10 x + 25 ) =
= 3 x² - 12 x + 12 - x² + 10 x - 25=
= 2 x² - 2 x - 13 =
= 2 ( x² - x + 1/4 - 1/4 ) - 13 =
= 2 ( x - 1/2 )² - 1/2 - 26/2 = 2 ( x - 1/2 )² - 27/2
Answer: D)