Complete the square: y = -2x^2 + 4x + 1 and graph it with 2 sets of points. Please show all your work.
(Don't worry about the graphing, I'll do that part)
Thank you
y = -2x^2 + 4x + 1
you want to start with +1x^2 , so factor out a -2 from the first 2 terms
y = -2[x^2 - 2x ] + 1
look at the x term, take 1/2 of its coefficient, then square it.
(1/2) of -2 is -1, and (-1)^2 = 1
add that insides the square bracket , then immediately subtract it again,
so in effect we have not changed the value of our expression.
y = -2[x^2 - 2x + 1 - 1 ] + 1
the first 3 terms inside the square brackets are now a "perfect square"
rewrite it as such
y = -2[(x-1)^2 - 1] + 1
distribute the -2 out front over the 2 terms inside the square bracket
y = -2(x-1)^2 + 2 + 1
last step:
y = -2(x-1)^2 + 3
all done