Asked by Hunter
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
(Don't worry about the graphing, I'll do that part)
Thank you
Answers
Answered by
mathhelper
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 <b>+ 1 - 1 </b>] + 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
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 <b>+ 1 - 1 </b>] + 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