MENU Polynomials & Beyond: A Precalculus Project : by - Mir Mahmood, Hasham Khawaja, & David Asis
Definition

  Definition
Sketching Graphs
Standard Form
Quadratic Equation

  The Leading Coefficient Test
Intermediate Value Theorem

 
Long Division
Division Algorithm
Synthetic Division
Remainder Theorem
Factor Theorem

  What is a Real Zero?
Descartes Rule
Rational Zero Test
Bounds : Upper & Lower

With the TI-82 Calculator, many things can be done easily. With the graphing calculator you can speed up many processes. However, please make sure you understand each concept and know how to do them manually before you use this resource.

(Please Note: Only Steps are given for the TI- 82, Buttons are in Green options are in Light Blue. )

To find Real zeros :

Find the real zero of 2x2 - 2

1. Press Y=
2. Enter the equation in the
Y= space
3. Press
Graph
4. Press 2nd , Trace.
5. Highlight option
2: Root and press enter.
6. When it prompts you for the
lower bound, move the trace cursor to the portion of the graph which is lower in value. For this equation, you would place it above the x-axis to the right because it is becoming negative on the left hand side.
6. When it prompts you for the
Upper bound, move the trace cursor to the portion of the graph which is higher in value. For this equation, you would place it below the x-axis to the left because it is becoming negative on the left hand side.
7. When the
guess prompt is given, press enter for yes.

NOTE: This was only one real zero, in this particular function, there are 2 real zeros. Find the other one by doing the same process through the other side.

Plotting the Inverse of a Function:

1. Enter the function in the
Y=
2. Press
Graph
3. Next press
2nd , PRGM
4. With the cursor buttons, highlite the option that says
DrawInverse.(DrawInv)
5. Press
Enter. Next on the screen you will see the command:
DrawInv
6. Press
2nd, VARS
7. Select the option which says
Function.
8. Select the Y= place you typed the function in. For example, in the very first step if you typed the function into
Y1, then at this screen you would also select Y1.
9. Press
enter and the inverse shall be graphed.

Finding the minimum or maximum value of a function

1. Enter the function in the
Y= and pressing GRAPH .
2. Press
2nd, TRACE and select option maximum or minimum. Then press enter.
3. For the
lower bound prompt, select the part of the graph which is lower in value. For a parabola, it will be to the left of the vertex.
4. For the
upper bound prompt, select the part of the graph which is higher in value. For a parabola, it will be to the right of the vertex.
5. When the
GUESS? prompt is given, press ENTER for yes.
6. The Bottom of the screen will then display the minimum or maximum of the given curve or function.

Finding a value of x.

(Using TRACE)

1. After entering the function in the Y= and then pressing GRAPH to graph it, press 2nd, TRACE.
2. Select the option which says
VALUE and press enter.
3. Then the screen will give you a prompt:
Eval X=

In this space, type in the value of x you wish to find out.

4. After typing the value, press enter.

(Using TABLE )

1. After entering the function in the Y= and then pressing GRAPH to graph it, press 2nd, TABLE.
2. Scroll up or down using the cursor keys to find the value of x you wish to know.
3. If you must scroll a lot, then do this:

a. PRess 2nd, WINDOW.
b. For
TblMin=, type in the value of x you wish to see first.
c. Press
2nd, TABLE to see the value of x you desire.


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