Determine the vertex and the axis of symmetry for the function below: y = -x2 + 2x + 1 a. vertex: (1, 2) axis of symmetry: y = 1 c. vertex: (2, 1) axis of symmetry: y = 1 b. vertex: (-1, 2) axis of symmetry: x = 1 d. vertex: (1, 2) axis of symmetry: x = 1

We are given the equation:

                           , whose solutions form a parabola.

Let, a, b, c represent respectively the coefficient of x^2, the coefficient of x, and the constant term.

Then the x-coordinate of the vertex can be found using the formula:
 
                                .

Thus, since a=-1 and b=2, the x-coordinate of the vertex is
. 

Plugging x=1 in , we find y=-1+2+1=0. Thus, the vertex is (1, 2).

The line of symmetry is the vertical line passing through the vertex, thus the line of symmetry is described by the equation x=1.

 vertex: (1, 2) axis of symmetry: x = 1

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