You can put this solution on YOUR website! Complete the square as an aid to graphing :
y = -x^2 + 2x + 2
:
We want the coefficient of x^2 to be +1. Mult equation by -1 and you have:
x^2 - 2x - 2 = 0
:
Write it in the form for completing the square:
:
x^2 - 2x + __ = +2
:
Find the value that completes the square; divide the coefficient of x by 2, and
square it, here it's -2; -2/2 = -1 and -1^2 is +1, add 1 to both sides:
:
x^2 - 2x + 1 = 2 + 1
:
x^2 - 2x + 1 = 3
or
(x-1)^2 = 3
:
Find the square root of both sides:
x - 1 = +/-Sqrt(3)
:
x = 1 + Sqrt(3)
and
x = 1 - Sqrt(3)
:
These two values will be the x intercepts of your graph which looks like this:
:
:
Note that 1 + Sqrt(3)is about +2.7 and 1 - Sqrt(3) is -.7, the x intercepts on
the above graph
:
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