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, –1.25); f(x) = x2 + x – 1

Axis of symmetry: x = 0.5; Vertex: (0.5, –1.25); f(x) = x2 – x – 1

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

Axis of symmetry: x = –0.5; Vertex: (–0.5, 1.25); f(x) = x2 – x – 1

The answer to your question is the third choice.

Step-by-step explanation:

The axis of symmetry is the dotted red line which is located in x = 1/2

The Vertex is the lowest point of the parabola which is (1/2, -1)

The equation of the function is:

                        (x - h)² = 4p(y - k)

-Substitution

                        (x - 1/2)² = 4p(y + 1)

-We can not know the value of p

                        x² - x + 1/4 = y + 1

Discarding choices, there are two possible answer, the second and the third choices, but because of the Vertex (0.5, -1), i think the right answer is the third choice.

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.