How do you determine if an equation is symmetric to the x-axis?

To check for symmetry with respect to the x-axis, just replace y with -y and see if you still get the same equation. If you do get the same equation, then the graph is symmetric with respect to the x-axis.

How do you determine if the graph is symmetric about the x-axis the Y axis or the origin?

1. X-Axis Symmetry: Occurs if “y” is replaced with “-y”, and it yields the original equation.
2. Y-Axis Symmetry: Occurs if “x” is replaced with “-x”, and it yields the original equation.
3. Origin Symmetry: Occurs if “x” is replaced with “-x” and “y” is replaced with “-y”, and it.

What graph is symmetric with respect to the x-axis?

A graph is said to be symmetric about the x -axis if whenever (a,b) is on the graph then so is (a,−b) . Here is a sketch of a graph that is symmetric about the x -axis. A graph is said to be symmetric about the y -axis if whenever (a,b) is on the graph then so is (−a,b) .

Can a function be symmetric about the x-axis?

Note: By definition, no function can be symmetric about the x-axis (or any other horizontal line), since anything that is mirrored around a horizontal line will violate the Vertical Line Test.

How do you find the symmetry of an equation?

If the vertex of a parabola is (k,l), then its axis of symmetry has equation x=k. We can find a simple formula for the value of k in terms of the coefficients of the quadratic. As usual, we complete the square: y=ax2+bx+c=a[x2+bax+ca]=a[(x+b2a)2+ca−(b2a)2].

What is symmetry of a graph?

A graph is symmetric with respect to a line if reflecting the graph over that line leaves the graph unchanged. This line is called an axis of symmetry of the graph. A graph is symmetric with respect to the y-axis if whenever a point is on the graph the point is also on the graph.

How do you tell if a function is symmetric about the origin?

Another way to visualize origin symmetry is to imagine a reflection about the x-axis, followed by a reflection across the y-axis. If this leaves the graph of the function unchanged, the graph is symmetric with respect to the origin.

How do you find the symmetry of a shape?

You can find if a shape has a Line of Symmetry by folding it. When the folded part sits perfectly on top (all edges matching), then the fold line is a Line of Symmetry.

What is symmetry types of symmetry?

The four types of symmetry are: Translation symmetry. Rotational symmetry. Reflection (or reflexive) symmetry. Glide symmetry.

Which graph will have symmetry about the x-axis?

A graph will have symmetry about the x x -axis if we get an equivalent equation when all the y y ’s are replaced with – y y. A graph will have symmetry about the y y -axis if we get an equivalent equation when all the x x ’s are replaced with – x x.

Why is the Y-axis of an equation not symmetric?

So, some terms have the same sign as the original equation and other don’t so there isn’t symmetry about the y y -axis. Finally, check for symmetry about the origin. Again, this is not the same as the original equation and isn’t exactly the opposite sign from the original equation and so isn’t symmetric about the origin.

How to find if the graph is symmetric about the origin?

Since the equation is not identical to the original equation, it is not symmetric to the y-axis. Check if the graph is symmetric about the origin by plugging in −x – x for x x and −y – y for y y. Solve for y y. Tap for more steps… Simplify ( − x) 3 ( – x) 3. Tap for more steps… Apply the product rule to − x – x.

Which equation is symmetric to the axis of the parabola?

1 Parabola is symmetric to the axis of the parabola. 2 If the equation has a y 2 term, then the axis of symmetry is along the x-axis. 3 If the equation has an x 2 term, then the axis of symmetry is along the y-axis.