Consider the following set of parametric equations. The title of this activity implies these parametric equations will not define a line segment, but you can verify that by finding three points and showing the change in [math]y[/math] over the change in [math]x[/math] is not constant.[br][br][math]x=t-1[/math][br][math]y=3+2t-t^2\text{ }0\le t\le3[/math][br]
Even though these parametric equations don't end up describing a line segment, they do still trace out the graph of some function. Eliminate the parameter to find this function. What is the domain of this function?
[math]y=3+2\left(x+1\right)-\left(x+1\right)^2[/math][br]or more simply:[br][math]y=-x^2+4[/math][br]The domain is [math]-1\le x\le2[/math]
Use your work to try to sketch the image of these parametric equations. Then check your work with the GeoGebra applet below. What do the arrow heads represent?