# How dones one flip the graph of a parametric curve?

• Bipolarity
In summary, the conversation discusses how to "flip" a parametric curve by reflecting it over the x-axis or y-axis. This is represented by negating the y-value in the parametric equations, resulting in either x = f(t) and y = -g(t) or x = -f(t) and y = g(t).

#### Bipolarity

How dones one "flip" the graph of a parametric curve?

Define the parametric curve C by
$x = f(t)$ and $y = g(t)$.

This curve can be plotted on the Cartesian plane. Let's say we "flipped" this curve over the x-axis, that is, we reflected every point on this curve about the x-axis so that the y-value for any given point has been negated.

How is the end result represented using the parametric equations shown above, assuming this is possible?

I would imagine just $x = f(t)$ and $y = -g(t)$ ?
And I assume similarly that a flip of the initial curve over the y-axis results in

$x = - f(t)$ and $y = g(t)$

BiP

That would be correct - you can easily test this by plotting a few simple relationships.

## 1. What does it mean to flip the graph of a parametric curve?

Flipping the graph of a parametric curve refers to reflecting the curve across a line, usually the x-axis or y-axis. This results in a mirror image of the original curve.

## 2. Why would someone want to flip the graph of a parametric curve?

Flipping the graph of a parametric curve can be useful for visualizing the properties of the curve, such as symmetry or periodicity. It can also be used to simplify equations or solve problems in mathematics and physics.

## 3. How is the graph of a parametric curve flipped?

The graph of a parametric curve can be flipped by multiplying one of the parameters by -1. For example, to flip the curve horizontally, multiply the x-parameter by -1, and to flip it vertically, multiply the y-parameter by -1.

## 4. Can any parametric curve be flipped?

Yes, any parametric curve can be flipped as long as it is defined and continuous for the given parameter values. However, the resulting flipped curve may not have the same properties as the original curve, such as symmetry or periodicity.

## 5. How does flipping a parametric curve affect its equation?

Flipping a parametric curve affects its equation by changing the signs of one or both of the parameters. This will result in a different function that may have different properties and solutions compared to the original curve.