Answer:
Step-by-step explanation:
For the given graph of the function, the correct answer is:
Axis of symmetry: x = -0.5
Vertex: (-0.5, 0.75)
f(x) = -x² + x
To determine the axis of symmetry, we look for the vertical line that divides the graph into two symmetric halves. In this case, the axis of symmetry is x = -0.5.
To find the vertex, we identify the coordinates of the highest or lowest point on the graph. The vertex is represented as (x, y), where x is the x-coordinate and y is the y-coordinate. In this case, the vertex is (-0.5, 0.75), indicating that the highest or lowest point of the graph occurs at x = -0.5 and y = 0.75.
Lastly, the formula for the function is given by f(x) = -x² + x. This means that for any given value of x, we can substitute it into the function to determine the corresponding value of f(x). In this case, the function is a quadratic function, represented by a downward-facing parabola.
It's important to note that the other options provided in the question do not match the given graph, as they have different equations and coordinates. The correct answer is the first option: Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = -x² + x.
