Parametric Equations

This section is currently under construction.

1. How do I graph a function of y?

Answer: Use parametric mode. In this mode, the button that usually types the variable X, will now type T.
Say you want to graph x=y^2. Press [MODE] followed by 3 down arrows and one right arrow and then [ENTER]. Then press [Y=]. For Y1T, key in the letter T (press the button that normally gives you X). Then for X1T, type in T^2. Then press the window button and change tmin so that it is negative. In general you should take a sample of t values which includes both positive and negative values. So t min should be negative and tmax positive.

2. How do I find the intersection of curves when the graphs are done in parametric mode?

Answer: If you are graphing explicit functions of y in parametric mode, say x=y^2 and x=4y, you can just switch the variables in the two equations to get y=x^2 and y=4x. Now graph these as functions of x and find the intersection the usual way. Here you will find that x=0 y=0 and x=4 and y=16 are solutions of this new set of equations. Reverse the values of x and y and you will get solutions of the original system. This doesn't change the first answer, x=0 y=0 but the second becomes x=16, y=4. There is also another case which can be done on the graphing calculator. This is the case where you are given a function of x, y=f(x) and a function of y, x=g(y). In this case you don't need parametric mode. Replace y in g(y) by f(x) to get x=f(g(x)). Then find the zeros of the x-f(g(x)). For all other cases, you need to solve two equations for two unknowns (the parameters). In this case, you can try using a program that is available on the Math Department website ( http://sard.math.qc.edu/ ). This program is known as Newton's Method for systems of equations. To find the program, click here. This program is for your information and use. You will never have to use it in a basic calculus course.




Related questions




Q1. How can I plot the graphs of y=f(x), y=f -1(x), and y=x on the same set of axes?




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