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.