The graph of a function is a visual representation of the relationship between the two variables, the x-axis and the y-axis. When a graph is symmetric, the two axes of symmetry divide the graph into two equal halves, creating a mirror image. In this article, we will examine the graph of the function f(x) = (x – 2)2 + 1 and determine its axis of symmetry.

## Examining The Graph

When we look at the graph of the function f(x) = (x – 2)2 + 1, we can see that it is a parabola. The parabola is in the shape of a U, with the vertex at the bottom of the U. The graph also has two lines of symmetry, one vertical line and one horizontal line.

## Determining The Axis Of Symmetry

The vertical line of symmetry is the axis of symmetry for the function f(x) = (x – 2)2 + 1. This means that the graph is symmetrical about the vertical line x = 2. The horizontal line of symmetry is the line y = 1, which is the y-intercept of the graph.

In conclusion, the graph of the function f(x) = (x – 2)2 + 1 has an axis of symmetry of x = 2. This line of symmetry divides the graph into two equal halves, creating a mirror image. Understanding the graph and its axis of symmetry is important for understanding the properties of the function.

When graphing an equation in the form of y = f(x), the concept of axis of symmetry provides an effective visual tool for understanding the function a representation. In particular, the graph of the function f(x) = (x – 2)2 + 1 can be constructed to clearly illustrate the axis of symmetry for this equation.

When graphing any given equation, the x-axis is always the axis of symmetry if the equation is written in the form y = f(x). In this case, f(x) = (x – 2)2 + 1, the variables are centered around x = 2. Thus, the equation has a vertical axis of symmetry at x = 2. To illustrate this, a graph of f(x) can be constructed, with the vertical axis of symmetry at x = 2 visualized as a horizontal line.

The graph of f(x) = (x – 2)2 + 1 is a parabola, with the vertex located at (2, 1). This vertex serves as a reference point for the axis of symmetry, and the parabola itself is symmetrical around the vertical line at x = 2. To the left of the vertical axis, the graph takes a negative parabolic shape, while to the right of the axis, the shape is positive.

To recap, the graph of f(x) = (x – 2)2 + 1 has an axis of symmetry located at x = 2, and the vertex of the graph is located at (2 , 1). Knowing this information regarding the graph of the equation is helpful in understanding the properties of the function and is a useful tool in forming a better visual representation.