Programming the Quadratic Formula into a TI-83/84+ Calculator

Once you know the quadratic formula, you can save time computing the roots (zeros) of quadratic polynomials by programming it into your Texas Instruments (TI) graphing calculator once-and-for-all.

To create a new program in your TI-83/84+, press PRGM, navigate over to the NEW menu, and select Create New. You’ll be asked to name your new program; the one in this guide is named QUAD, but you can name yours whatever you want. Once you enter the name you should see a Program Editor screen like this where you’ll write the program. That lonely colon : indicates the beginning of a line of code.

PROGRAM:QUAD \\ :
TI-83+ Screenshot: the QUAD program, empty for now.

Given a quadratic polynomial \(ax^2 + bx + c\) your program will need to do three things: first prompt you to input the coefficients \(a\) and \(b\) and \(c\), then calculate the roots using the quadratic formula, and then display those roots on the home screen.

  1. Prompting for the Coefficients

    While in the Program Editor, pressing PRGM will present you with menus of programming-related keywords. We’re interested in input/output keywords, so press PRGM and navigate over to the I/O menu. Select Prompt and enter Prompt A,B,C as the first line of your program. Now when the program is executed, it will prompt for values of A and B and C to be entered. Note that the comma , button is above the 7 button.

  2. Calculating the Roots

    The roots \(x\) of a quadratic polynomial are \[ x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} \,. \] It’ll make for a cleaner program if you only compute that square root once, and store it to a variable, say D. \[ x = \frac{-b \pm D}{2a} \quad\text{where } D = \sqrt{b^2-4ac} \] The syntax for storing this value to D is √(B²−4AC)→D, where you can enter that arrow → by pressing the STO→ button. It will be convenient to store the two roots to variables after calculating them. We’ll store the first root to R and the other root to T, which stand for “Root” and “The other root” respectively. Do this with the lines (-B−D)/(2A)→R and (-B+D)/(2A)→T.

  3. Displaying the Roots

    Finally to display the roots, return to the menu of input/output keywords by pressing PRGM and selecting the I/O menu. Select Disp then enter the line Disp R,T to display the roots.

Once finished your program should look like this:

PROGRAM:QUAD \\ :Prompt A,B,C \\ :√(B²-4AC)→D \\ :Disp (-B-D)/(2A) \\ :Disp (-B+D)/(2A)
TI-83+ Screenshot: the QUAD program 
: Prompt A,B,C
: √(B²−4AC)→D
: (-B−D)/(2A)→R
: (-B+D)/(2A)→T
: Disp R,T

To finish up, you should test your program on a quadratic polynomial with roots that you know to make sure you’ve entered the code correctly. To run your freshly written program, press PRGM and find QUAD under the EXEC menu. Selecting it will show prgmQUAD on the home screen; press ENTER to run prgmQUAD. Referring to the quadratic polynomial \[ 6(x-28)(x-496) \;\;=\;\; 6x^2 - 3144x + 83328 \] enter A\(=6\), B\(=-3144\), and C\(=83328\).

pgrmQUAD \\ A=?6 \\ B=?-3144 \\ C=?83328 \\ \\ 28 \\ 496 \\ Done
TI-83+ Screenshot: testing the QUAD program

Delightful! Note that if you ever run this program and receive the error ERR:NONREAL ANS, this indicates that the roots of the quadratic are not real. I.e. \(ax^2+bx+c\) does not factor over the real numbers. If you’d like to change the mode of your calculator to display complex numbers rather than report an error, press MODE and select a+bi.

For more information on programming in your TI calculator, consult the programming section in your calculator’s guidebook.