Finding Points for Graphing a Function with a TI-83/84

Website
Home
Mobile Pages Index

© 2003 Frank Kizer

**General:**

This procedure is aimed at finding ordered pairs to
graph a function by hand. There are several methods for doing that with a
calculator, but they require several operations that are not intuitive.
So, students often forget the procedure of the more non-intuitive methods. We
will use only the graphing and TRACE functions.

**Preliminaries:
**We will demonstrate how to find general coordinates
of points for graphing a linear equation in two variables. We will then
find the coordinates for the specialized method of the intercept method.
Finally, we will find the points for graphing a parabola.

Let's choose x-values -2, 0, 3 as indicated in the completed table below.

x |
y |

-2 | -1 |

0 |
1 |

2 |
3 |

Now graph the points and draw a straight line through them.

**Method for Graphing with Intercepts:
**Let's graph the equation 2x+3y=3.

d) Press TRACE and then 0, ENTER to get y=1.

x=1.5, y=0 for the x-intercept.

**Method for Graphing a Parabola:
**Let’s find the points for graphing the following
equation for a parabola f(x) = 2x

a. First we should find the x-coordinate for the

vertex of the parabola since that gives us a good starting place to locate additional points. That coordinate can be found with the

following equation: x=-b/2a (Where “a” is the number in front of the x

a) From the home screen of the calculator enter -(-4)/(2*2) to get 1. The two signs in front of 4 are made with the (-) key on the calculator.

Plug that value, 1, into the equation quadratic equation to get 2(1)

your table of values.

First graph the equation:

a) Press Y= (Located at the left end of the screen.), and clear any equations already entered by using the CLEAR button.

b) Press, the [X,T,θ, n] button to enter x. Then press the x

c) Press – (the minus sign), 4, X , +1. You should now have 2X

d) Press GRAPH to graph the equation and when the graph appears press TRACE. (Trace is one of the buttons immediately below the screen.)

Now find the points:

a) Press ZOOM; then press 4 for ZDecimal. If the vertex of the parabola is not on the screen press ZOOM, 3 for ZoomOut. Move the cursor until

you are on the center of the screen, x=0, y=0 and press ENTER.

b) Press TRACE and then move the cursor along the graph until you are near the vertex. Carefully move the cursor through the vertex until you

get to x=1, y=-1. Note that if you move the cursor to either side of that value, the absolute value of y= will be smaller. Let’s enter these

values in a table; then calculate more points.

x |
y |

-1 |
7 |

0 |
1 |

1 |
-1 |

2 |
1 |

3 |
7 |

c) Enter 0 and press ENTER to get y=1; then press -1,
ENTER to get 7. Note that by symmetry, the value for x=2 is the same as
for x=0 and the

value for 3 is the same as for -1.

d) Enter the values on a coordinate system and sketch the graph through
the points.

*Released: 4/12/12
Last Revised: 4/7/13 *