Desmos Graphing Calculator Tips for Algebra 1 (Part 1)

Steve Boring
7 May 201915:01

TLDRThis video offers Desmos graphing calculator tips tailored for Algebra 1, aligning with Virginia State Standards. It covers graphing equations, inequalities, systems of equations, and finding zeros or x-intercepts. The tutorial demonstrates how Desmos simplifies graphing compared to traditional calculators, allowing equation input in any form. It also addresses the use of sliders for variable input, navigating function forms, and handling errors with x and y variables. The presenter promises a follow-up video on regression techniques.

Takeaways

  • 📊 Desmos is a powerful graphing calculator that simplifies graphing equations in various forms compared to traditional graphing calculators.
  • 🔢 Graphing equations on Desmos is straightforward; you can input equations directly without needing to solve for y, unlike some other graphing calculators.
  • ➖ For inequalities, Desmos allows you to input them with the appropriate symbols and will shade the region satisfying the inequality.
  • 🔄 Substitution can be tricky on Desmos; using sliders for variables can help find specific outputs from equations.
  • 🔢 When substituting, avoid using x and y directly in functions; instead, use variables like a and b or x1 and y1 to avoid errors.
  • 📈 Systems of equations can be graphed simultaneously on Desmos, making it easy to find their intersection points.
  • 🔍 Finding roots or zeros (x-intercepts) on Desmos is done by setting the equation to zero and identifying the points where the graph crosses the x-axis.
  • 📋 Desmos offers a table feature that can be used to input domains and find corresponding ranges for functions.
  • 📉 Desmos is not just for graphing; it also allows for performing operations like finding cube roots and other complex calculations within the graphing interface.
  • ⏱ The video is part of a series, with part two focusing on regression, indicating that Desmos has capabilities for statistical analysis as well.

Q & A

  • What are some Desmos graphing calculator tips for Algebra 1?

    -The Desmos graphing calculator tips for Algebra 1 include graphing equations in any form, using sliders for variables, handling inequalities, and finding roots or zeros of functions.

  • How does the Desmos graphing calculator handle graphing equations?

    -Desmos allows you to graph equations in any form, which is more user-friendly than traditional graphing calculators that often require equations to be in function form.

  • What is the difference between using Desmos for graphing and a traditional graphing calculator?

    -Desmos is easier to use for graphing as it allows equations to be inputted in any form, whereas traditional calculators like TI require equations to be solved for y.

  • How do you graph inequalities in Desmos?

    -To graph inequalities in Desmos, you input the inequality as you would an equation, but use the appropriate inequality symbol (e.g., less than or equal to).

  • What is a common issue when using Desmos for substitution problems?

    -A common issue with substitution in Desmos is that using x and y directly can cause errors; it's often necessary to use variables like a and b or to specify x1, y1, etc., to avoid these errors.

  • How can you find the value of an algebraic expression using Desmos?

    -You can find the value of an algebraic expression in Desmos by using sliders for variables and then inputting the expression to see the output.

  • What is the process for finding the roots or zeros of a function in Desmos?

    -To find the roots or zeros of a function in Desmos, you input the function's equation and set y to zero, then Desmos will highlight the x-intercepts where the function crosses the x-axis.

  • How do you handle systems of equations in Desmos?

    -In Desmos, you graph both equations of the system and find the solution by looking at the point of intersection of the two lines.

  • Why might Desmos give an error when trying to input a function in the form f(x)?

    -Desmos might give an error when inputting a function in the form f(x) if it's expecting an equation to be graphed rather than a specific value. To resolve this, you can use x1, y1, or change the variable names.

  • What is the purpose of using sliders in Desmos for algebra problems?

    -Sliders in Desmos allow you to easily adjust the values of variables and see the resulting changes in the algebraic expressions or graphs, which is helpful for exploring and solving problems interactively.

Outlines

00:00

📈 Desmos Graphing Calculator Tips for Algebra 1

This paragraph introduces a video tutorial focused on Desmos graphing calculator tips tailored for Algebra 1, aligning with the Virginia State Standards of Learning. The narrator discusses various topics such as graphing equations, substitution, systems of equations, inequalities, finding zeroes, roots, and x-intercepts. It also mentions a follow-up video on regression due to time constraints. The Desmos graphing calculator is praised for its ease of use compared to traditional graphing calculators, especially for graphing equations in any form without needing to solve for y. The tutorial also guides viewers on how to access the Desmos calculator, particularly for students who might be using it for standardized testing.

05:03

🔢 Advanced Desmos Features for Algebraic Expressions

The second paragraph delves into more advanced features of Desmos for algebraic expressions. It covers how to input complex equations, including cube roots and sliders for variables, to dynamically see the results of algebraic manipulations. The narrator demonstrates how to use the nth root function to input cube roots and how to use sliders to adjust variable values and observe the output. The paragraph also addresses a common issue with Desmos when using x and y variables directly, suggesting workarounds such as using subscripts or changing variable names. The tutorial shows how to input specific function values, like f(-8), and how to handle multiple outputs, such as finding a range from a given domain using tables.

10:07

🧩 Solving Systems and Finding Roots with Desmos

The final paragraph covers solving systems of equations and finding roots or x-intercepts using Desmos. It explains that systems of equations can be solved graphically by finding the intersection points of two equations. The tutorial also touches on how to approach word problems that require setting up equations before solving them. Lastly, it demonstrates how to find roots or x-intercepts by setting y or f(x) to zero and using Desmos to identify the points where the equation equals zero. The narrator provides a brief preview of an upcoming video part two, which will focus on regression techniques.

Mindmap

Keywords

💡Graphing Equations

Graphing equations refers to the process of plotting mathematical equations on a graph to visualize their solutions. In the context of the video, graphing equations is one of the primary functions of the Desmos graphing calculator. The video demonstrates how to input equations directly into Desmos, even in standard form, and view their graphical representations. This is showcased when the instructor types '4x + 5y = -20' into Desmos, and the calculator plots the corresponding linear equation.

💡Substitution

Substitution is a method used in algebra to solve equations by replacing a variable with an expression or value. The video explains how to use substitution in Desmos by providing an example where the instructor solves for one variable in terms of another and then inputs these values into the calculator to find the solution. This technique is crucial for solving systems of equations and understanding the relationship between different variables.

💡Systems of Equations

A system of equations is a set of two or more equations that are solved simultaneously. The video touches on how to graph systems of equations in Desmos, which involves plotting each equation and finding the point of intersection, known as the solution to the system. The instructor briefly mentions that the SOL (Standards of Learning) might present word problems that require setting up and solving systems of equations.

💡Inequalities

Inequalities are mathematical statements that show a relationship where one quantity is not equal to another. In the video, the instructor discusses graphing inequalities on Desmos, which involves using symbols like 'less than' or 'greater than'. The script includes an example where the instructor types '2/7x - 2 ≤ 0' into Desmos to demonstrate how to graph an inequality and identify the correct shaded region representing the solution set.

💡X-intercepts

X-intercepts, also known as roots or zeros, are the points where a graph of an equation crosses or touches the x-axis. The video explains how to find x-intercepts in Desmos by setting the equation to equal zero and graphing it. An example given is '3x^2 + 11x = 20', where the instructor demonstrates how to input the equation and identify the x-intercepts on the graph.

💡Desmos Graphing Calculator

The Desmos Graphing Calculator is an online tool that allows users to plot and manipulate graphs of mathematical functions and equations. Throughout the video, the instructor uses Desmos to illustrate various algebraic concepts, emphasizing its ease of use compared to traditional graphing calculators. Desmos is highlighted for its ability to graph equations in any form and its interactive features, such as sliders and tables.

💡Virginia State Standards of Learning

The Virginia State Standards of Learning (SOL) are a set of academic standards that outline what students should know and be able to do at the end of each grade level. The video is specifically aligned with these standards, focusing on algebraic concepts that are relevant to students in Virginia. The SOL is mentioned as a framework for the types of problems and skills covered in the tutorial.

💡Regression

Regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. Although not fully covered in the provided script, the video mentions that part two will cover regression, including linear and quadratic regression, which are techniques for fitting a line or curve to a set of data points. This suggests that the video series aims to provide a comprehensive view of algebraic graphing and data analysis tools in Desmos.

💡Function Form

Function form refers to the way a mathematical function is expressed, typically with a dependent variable defined in terms of one or more independent variables. In the video, the instructor discusses entering equations in function form into Desmos, such as 'f(x) = 11(x - 24) / 2', to find specific outputs for given inputs. This is important for understanding how to use Desmos to evaluate functions at particular points.

💡Sliders

Sliders in Desmos are interactive controls that allow users to input and adjust values dynamically. The video demonstrates how to add sliders to an equation to easily explore how changes in one variable affect the output. For instance, the instructor adds sliders for variables 'a' and 'b' in an equation to show how the value of the expression changes as 'a' and 'b' are adjusted, providing a visual and interactive way to understand algebraic relationships.

Highlights

Desmos graphing calculator is easier to use than traditional graphing calculators for algebra 1 students.

Desmos allows graphing equations in any form, not just function form.

The video demonstrates how to access and use the Desmos graphing calculator for Virginia State Standards of Learning.

Graphing equations on Desmos is as simple as typing them in.

Desmos differentiates between a negative sign and a subtraction sign.

Inequality graphs on Desmos require an extra step for the less than or equal to symbol.

Desmos provides a visual toggle to turn graphs on and off.

Substitution can be tricky in Desmos, especially when using x and y variables.

Desmos offers sliders for algebraic expressions to see the value changes dynamically.

The video explains how to correctly input cube roots and other functions in Desmos.

Desmos can handle function form equations and provide outputs for specific inputs.

Systems of equations on Desmos are solved by graphing both equations and finding their intersection.

Desmos can graph roots or zeros of a function by setting y or f(x) to zero.

The video will have a part 2 focusing on regression for more advanced topics.

Desmos is a powerful tool for algebra 1 students, especially for graphing and solving equations.