How to program the quadratic formula into a TI-84 or TI-84 Plus CE

The Glaser Tutoring Company
2 Oct 202204:03
EducationalLearning
32 Likes 10 Comments

TLDRIn this tutorial from Glazer Tutoring, learn how to program your TI-83 or 84 calculator to solve quadratic equations efficiently. The guide walks you through creating a 'quad' program, inputting coefficients a, b, and c, and using the quadratic formula to find roots. It simplifies the process of solving equations like x^2 + 6x + 9, demonstrating how to input values and retrieve roots as -3. This saves time and effort, making complex calculations a breeze. The video also encourages viewers to explore more educational content on their channel covering various subjects.

Takeaways
  • 📚 Today, we'll learn how to program the quadratic function on a TI-83 or TI-84 calculator.
  • 🔧 Start by accessing the 'program' function and creating a new program named 'quad'.
  • 🔢 Ensure the calculator handles complex numbers by selecting the a+bi mode from the catalog.
  • 📊 Use the 'prompt' command to input values for a, b, and c, which are the coefficients of the quadratic equation.
  • 📐 Enter the formula for the quadratic equation's roots, storing results in variables D and E.
  • 🔄 Repeat the process for both positive and negative roots, ensuring accurate calculation.
  • 📟 Use the 'display' function to show the results of the calculations on the screen.
  • 📝 Test the program with an example quadratic equation: x² + 6x + 9, where a=1, b=6, and c=9.
  • 🔍 Running the program with the example values will show the roots of the equation: -3 and -3.
  • 🎥 Check out the Glazer Tutoring channel for more educational videos on physics, chemistry, biology, and mathematics.
Q & A

  • What is the purpose of programming the TI-83 or TI-84 calculator with the quadratic function?

    -Programming the calculator with the quadratic function saves time by quickly calculating the roots of quadratic equations.

  • How do you start creating a new program on the TI-84 calculator?

    -To start creating a new program, press the 'Program' button, then hit 'Enter' to select 'Create New Program', and enter a name for the program.

  • Why is it necessary to handle complex numbers in the program?

    -Handling complex numbers is necessary to ensure the program can correctly process and display solutions that include complex roots.

  • What is the significance of the 'a', 'b', and 'c' values in the quadratic function program?

    -The 'a', 'b', and 'c' values are the coefficients of the quadratic equation, representing the coefficients of x^2, x, and the constant term, respectively.

  • How do you input the quadratic formula into the program?

    -Input the quadratic formula by entering the expression for the roots: (-b + sqrt(b^2 - 4ac)) / (2a) and (-b - sqrt(b^2 - 4ac)) / (2a), and store these values in variables 'd' and 'e'.

  • What does the 'prompt' function do in the context of this program?

    -The 'prompt' function asks the user to input values for 'a', 'b', and 'c', which are then used in the calculations for the quadratic formula.

  • How do you display the results of the quadratic function on the calculator?

    -To display the results, use the 'Display' function to show the values stored in 'd' and 'e', which represent the roots of the quadratic equation.

  • What are the steps to run the completed quadratic function program?

    -To run the program, clear the screen, go to 'Program', select and execute the 'quad' program, input the values for 'a', 'b', and 'c' when prompted, and view the displayed roots.

  • How are the values 'a', 'b', and 'c' determined in a sample quadratic equation?

    -The values 'a', 'b', and 'c' are determined from the coefficients of the terms in the quadratic equation. For example, in x^2 + 6x + 9, 'a' is 1, 'b' is 6, and 'c' is 9.

  • What is the final output of the quadratic function program for the sample equation x^2 + 6x + 9?

    -The final output for the sample equation x^2 + 6x + 9 is the roots -3 and -3, indicating the equation has a double root at x = -3.

Outlines
00:00
📚 Programming the Quadratic Function on TI-83/84 Calculators

This paragraph provides a step-by-step tutorial on how to program a TI-83 or 84 calculator to solve quadratic equations. The process begins by accessing the program menu and creating a new program named 'quad'. It then guides the user through the process of handling complex numbers by selecting 'a + bi' from the catalog. The script continues with instructing the user to prompt for the coefficients 'a', 'b', and 'c' of the quadratic equation. The core of the programming involves entering the formula for the quadratic roots, which includes terms like '-alphaB + sqrt(alphaB^2 - 4*alphaA*alphaC)', divided by '2*alphaA'. The roots are stored in variables 'alphaD' and 'alphaE'. The final step is to display the calculated roots. The tutorial also includes an example of how to use the program with a specific quadratic equation, x^2 + 6x + 9, which results in the roots being -3. The video concludes by encouraging viewers to check out the channel for more educational content.

Mindmap
Keywords
💡TI 83/84 Calculator
The TI 83 and TI 84 are graphing calculators produced by Texas Instruments. They are widely used in educational settings, particularly for mathematics and science. In the video, the TI 83/84 calculators are the primary tools for programming a quadratic function, which is the main focus of the tutorial. The script details the steps to program these calculators, highlighting their utility in solving mathematical problems.
💡Quadratic Function
A quadratic function is a polynomial function of degree two. It is generally represented as f(x) = ax^2 + bx + c, where a, b, and c are constants, and x is the variable. The video script teaches viewers how to program a quadratic function into a calculator, which is essential for solving quadratic equations and finding their roots.
💡Programming
Programming, in the context of the video, refers to the process of inputting a set of instructions into a calculator to perform a specific task, such as calculating the roots of a quadratic equation. The script provides a step-by-step guide on how to program the calculator, emphasizing the importance of following the instructions carefully.
💡Complex Numbers
Complex numbers are numbers that consist of a real part and an imaginary part, usually written in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit. In the script, the tutorial includes handling complex numbers when programming the quadratic function, which is important for solving equations that do not have real solutions.
💡Coefficients
In the context of a quadratic equation, coefficients are the numerical factors multiplying the variables. The script mentions 'a', 'b', and 'c' as the coefficients of the quadratic equation, which are essential for determining the roots of the equation when programmed into the calculator.
💡Quadratic Equation
A quadratic equation is an equation of the second degree, typically in the form ax^2 + bx + c = 0. The video script explains how to program a calculator to find the roots of a quadratic equation, which are the values of x that satisfy the equation.
💡Roots
Roots, also known as zeros or solutions, are the values of the variable that make the quadratic equation equal to zero. The script demonstrates how to use the programmed calculator to find these roots, which is the ultimate goal of solving a quadratic equation.
💡Catalog
In the context of the TI calculator, the catalog refers to a menu of built-in functions and commands that can be used in programming. The script guides the user through navigating the catalog to select necessary functions for programming the quadratic function.
💡Prompt
Prompting in the script refers to the action of asking the user to input values for the variables 'a', 'b', and 'c' of the quadratic equation. This is a crucial step in the programming process as it allows the user to input the specific coefficients of the equation they wish to solve.
💡Execution
Execution in the context of the video means running the programmed quadratic function on the calculator to perform the calculations. The script explains how to execute the program after it has been entered, which leads to finding the roots of the given quadratic equation.
💡Display
Display in the script refers to the action of showing the results of the calculation on the calculator's screen. After programming and executing the quadratic function, the calculator will display the roots, which is the final output the user is looking for.
Highlights

Introduction to programming the TI-83 or 84 calculator with a quadratic function.

Starting the process by accessing the program menu on the calculator.

Creating a new program and naming it 'quad' for the quadratic function.

Navigating to the Second catalog to handle complex numbers.

Selecting 'a + bi' from the catalog to work with complex numbers.

Prompting the user to input coefficients a, b, and c for the quadratic equation.

Using the 'prompt' command to request input for variables a, b, and c.

Entering the formula for the quadratic equation in the calculator's programming environment.

Calculating the discriminant (b^2 - 4ac) under the square root.

Storing the calculated values in variables Alpha D and Alpha E.

Using the 'display' command to show the roots of the quadratic equation.

Finalizing the program without clearing it, using 'Second quit'.

Executing the 'quad' program to find the roots of a given quadratic equation.

Demonstrating the program with a sample quadratic function x^2 + 6x + 9.

Inputting the coefficients a=1, b=6, and c=9 into the program.

Revealing the roots of the sample quadratic equation as -3, -3.

Conclusion and invitation to explore more educational content on the Glazer Tutoring channel.

Transcripts

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