Which graph represents the equation y = – (x – 1)2 + 1? On a coordinate plane, a parabola opens up. It goes through (0, 2), has a vertex at (1, 1), and goes through (2, 2).
On a coordinate plane, a parabola opens down. It goes through (0, 0), has a vertex at (1, 1), and goes through (2, 0).
On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (negative 1, 1), and goes through (0, 0).
On a coordinate plane, a parabola opens up. It goes through (negative 2, 2), has a vertex at (negative 1, 1), and goes through (0, 2).

Step-by-step explanation:

Compare the given equation  y = -(x - 1)^2 + 1  to y - k = a(x - h)^2.

Please be sure to use " ^ " to indicate exponentiation.

Through this comparison, we see that h = 1 and k = 1.  Thus, the vertex is at (1, 1).

Because of the - sign in front of (x - 1), we know that the parabolic graph opens down.  Thus we must eliminate answers 1 and 4.

Look at Answer 2:  (0, 0) is the origin.  Does the graph go through this point?  Let x = 0 and find y.  y = (0 - 1)^2 + 1 = 2.  No, graph does not go through (0, 0).

Look at Answer 3:  Is (2, 0) on the graph?  Is (-1, 1) the vertex?  First we get from y = -(x - 1)^2 + 1 the particular values 1 = -(2 - 1)^2 + 1, or

                                                                     1 = -2 + 1   No.

Look at Answer 5:  Is (-1, 1) the vertex, and does the graph go through (0, 2)?

y = -(x - 1)^2 + 1  =>  2 = (0 - 1)^2 + 1   this is TRUE and so the fifth answer is the correct one.

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: