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

A. Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 – x – 1

B. Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 + x – 1

C. Axis of symmetry: x = –0.5; Vertex: (–0.5, –0.75); f(x) = –x2 + x – 1

D. Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 + 2x – 1

Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 + x – 1

Step-by-step explanation:

The answer is A because the axis of symmetry is in between 0 and 1, the vertex lies on 0.5 and -0.75, and the parabola opens down so the coefficient of a is -1, and the y-int or the value of c is -1

The vertex of the function is  axis of symmetry is  and the formula for the function is  Option (a) is correct.

Further Explanation:

Given:

Calculation:

The standard form of the parabola is shown below.

Here, the parabola has vertex at  and has the symmetry parallel to x-axis and it opens left.

The general form of the parabola can be expressed as follows,

The graph is a downward parabola.

From the graph it has been observed that the vertex of the parabola is

Symmetry of the graph is  

The -intercepts of the graph is  Therefore, the value of is  

The value of  is -1 as the graph is a downward parabola.

The vertex of the function is  axis of symmetry is  and the formula for the function is  Option (a) is correct.

Learn more:

1. Learn more about unit conversion

2. Learn more about non-collinear

3. Learn more aboutbinomial and trinomial

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Conic sections

Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola.