Collaborative effort by Adeya Powell and Laura Trkovsky

Parametric Curves

Graph

for some appropriate range for t.

Interpret. Is there anything to vary to help understand the graph?

LetÕs start making some conjectures:

I believe the graph will be line because t+1 and 2t+1 are both graphs of a line.

LetÕs see if we can line the x and y intercepts:

Y=mx+b is the slope intercept form of a line.

therefore, 2t-1=m*(t+1) +b

Finding the y-intercept:

x=0 when t=-1

when x=0, b=2t-1 but t=-1, therefore b=-3.

(0,-3) is the y intercept.

Where does the line? hit the x-intercept:

Y=0 when t=1/2

X=1/2 +1=1.5

(1.5,0)

LetÕs now look at the graph,

We were correct about the intercepts. The t values went from

-4É4. So the y values would go from -9É7.

If we increase the values for t, we would lengthen the line. If we decrease the value for t, we would shorten the line.

-2É2