For the graph of the function, identify the axis of symmetry, vertex and the formula for the function.

Axis of symmetry: x = –0.5; Vertex: (–0.5, –0.5); f(x) = –2x2 + 2x – 1

Axis of symmetry: x = 0.5; Vertex: (0.5, –0.5); f(x) = 2x2 – 2x – 1

Axis of symmetry: x = –0.5; Vertex: (–0.5, 0.5); f(x) = –2x2 + 2x – 1

Axis of symmetry: x = –0.5; Vertex: (–0.5, –0.5); f(x) = –2x2 – 2x – 1

Description

We know that this is a parabola, as the equation is denoted by the x^2 term.

We can see that the symmetry is seen at the point -0.5, therefore making the axis of symmetry the vertical line -0.5.

The vertex is found in quadrant three. In other words, it will shift by a negative value both horizontally and vertically. The vertex is therefore (-0.5, -0.5).

We can verify this in the equations by using the formula (-b/2a) to find the vertex. The only quadratic equation that satisfies this is -2x^2 + 2x -1.

To sum it up, the answers are:

-2x^2 + 2x - 1.

AoS: x = -0.5

Vertex: (-0.5, -0.5).