Question

Which of the following answer choices expresses the axis of symmetry and the vertex of the function shown in the image

A. x=2; (2,4)
B. x=1; (1,7)
C. x=1; (1,5)
D. x=-1; (-1,1)

Answer 1

C. x = 1; (1, 5).

Explanation:

1. Axis of symmetry: The axis of symmetry is a vertical line that divides the graph into two symmetric parts. It passes through the vertex of the parabola.

2. Vertex: The vertex is the highest or lowest point on the graph of a quadratic function. It represents the minimum or maximum value of the function.

By analyzing the graph in the image, we can see that the axis of symmetry appears to be a vertical line passing through x = 1. This means that the correct answer choice for the axis of symmetry is x = 1.

To find the vertex, we need to determine the corresponding y-coordinate. By looking at the graph, we can see that the vertex appears to be the point (1, 5). This means that the correct answer choice for the vertex is (1, 5).