Exploring Y-Axis Symmetry in Mathematics: Criteria and Observations to Determine Graph Symmetry

symmetric with the y-axis

When a graph is symmetric with respect to the y-axis, it means that the graph has a property of reflection symmetry about the y-axis

When a graph is symmetric with respect to the y-axis, it means that the graph has a property of reflection symmetry about the y-axis. This means that if you draw a vertical line through the y-axis, the graph on one side will be the mirror image of the graph on the other side.

To determine if a graph is symmetric with the y-axis, you can try using the following criteria:

1. Function Definition: If the function definition involves only even powers of x and does not have any odd powers or terms with coefficients that are odd, then the graph will be symmetric with the y-axis.

For example, the function f(x) = x^2 – 4x + 3 is symmetric with the y-axis because it only has even powers of x (x^2) and no odd powers or coefficients.

2. Equation Analysis: If you have an equation or an equation of a curve (such as a conic section), you can examine its properties to determine if it is symmetric with the y-axis.

For example, the equation of a circle centered at the origin is x^2 + y^2 = r^2. Because the equation involves only even powers of x and y, the graph of the circle is symmetric with respect to the y-axis.

3. Graph Observation: You can also determine symmetry by observing the graph itself. If the graph appears identical on both sides of the y-axis when folded, then it is symmetric with the y-axis.

For example, the graph of a quadratic function y = x^2 – 3x + 2 is symmetric with the y-axis because when you fold the graph along the y-axis, the left side will coincide with the right side.

Remember, checking for y-axis symmetry is important in math as it helps in understanding the properties of functions and curves, and in graphically analyzing equations.

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