Part 1: Use Desmos to Ace the SAT
TLDRThis tutorial video demonstrates how to utilize Desmos, a graphing calculator, to tackle questions on the digital SAT. It covers Desmos' functionalities, such as graphing equations, adjusting axis steps, and using sliders for variables. The video illustrates solving problems involving the intersection of graphs, finding x-intercepts, and determining the value of constants for specific conditions. It showcases Desmos' efficiency in solving complex equations and quadratic problems, offering a visual approach to simplify the SAT preparation process.
Takeaways
- 🌐 Desmos is a powerful graphing calculator that can be used to assist with solving questions on the digital SAT.
- 📈 Users can easily graph functions on Desmos by typing them directly into the calculator, such as '3x - 5' or '3x^2' for quadratic functions.
- 🔢 Desmos supports various mathematical operations, including exponents, which can be input using the shift key followed by the number key.
- 🖊️ The color of the graphed functions can be customized through the settings, offering a visual distinction between different equations.
- 🔄 The 'home' button resets the graph to the default zoom, which is helpful for re-centering after extensive zooming or scrolling.
- 🔧 Users can adjust the axis settings, including the range and step of the x and y-axes, to better visualize and understand the graph.
- ⚙️ Desmos allows for the input of complex equations, and if the graph doesn't appear, removing 'equals zero' from the equation can resolve the issue.
- 🎚️ Sliders can be added for variables in equations, providing an interactive way to see how changes in the variable affect the graph.
- 🔍 Desmos can be used to find the exact point of intersection between two graphs, which is useful for solving SAT problems involving systems of equations.
- 📝 For SAT problems, Desmos can be particularly helpful with quadratics and systems of equations, where the intersection points are critical to the solution.
- 💡 Desmos is not just limited to complex problems; it can also simplify solving simple linear equations by graphically representing where the equation crosses the x-axis.
Q & A
What is the main topic of the video?
-The main topic of the video is how to use Desmos, a graphing calculator, to help answer questions on the new digital SAT.
How can Desmos be accessed for use?
-Desmos can be accessed by visiting desmos.com/calculator or by searching for 'Desmos graphing calculator' on Google.
What is the default screen of Desmos used for?
-The default screen of Desmos is used for graphing mathematical functions and equations.
How do you graph a basic function like 3x - 5 on Desmos?
-You can graph a basic function like 3x - 5 by simply typing it into the input field on Desmos.
How do you enter an exponent in Desmos?
-To enter an exponent in Desmos, you press the shift key and then the number key corresponding to the exponent.
What is the purpose of the home button in Desmos?
-The home button in Desmos resets the graph to the default zoom level, which is useful after zooming in or out.
How can you change the color of a graphed function in Desmos?
-You can change the color of a graphed function by clicking the gear icon (settings) and selecting a new color from the options provided.
What does the wrench icon in Desmos allow you to do?
-The wrench icon in Desmos allows you to change various settings, such as turning grid lines on or off, and adjusting the x-axis and y-axis ranges and steps.
Why might Desmos not graph an equation when you first enter it?
-Desmos might not graph an equation when you first enter it if the equation is set equal to zero, as Desmos requires an implicit equation of x and y.
How can you find the value of C in the equation 2y = C when it intersects a parabola at exactly one point?
-You can find the value of C by graphing the parabola and the line 2y = C on Desmos and adjusting the value of C with a slider until the two graphs intersect at exactly one point.
What is a slider in Desmos and how is it used?
-A slider in Desmos is a tool that allows you to adjust the value of a variable in an equation to see how it affects the graph. It's used to find specific values that satisfy certain conditions, such as intersection points.
How does Desmos help in solving problems related to quadratics on the SAT?
-Desmos helps in solving problems related to quadratics by allowing you to graph the quadratic equation and other related equations to visually determine the solution.
What is an example of a simple equation problem that can be solved using Desmos?
-An example of a simple equation problem that can be solved using Desmos is 4x - x = x + 9, where Desmos can show the solution by graphing and finding the x-intercept.
Outlines
📈 Introduction to Desmos and Graphing Basics
The video begins with an introduction to Desmos, a graphing calculator accessible at desmos.com. The presenter demonstrates how to graph basic functions like 3x - 5 and 3x^2 by typing them directly into Desmos. The functionality to change the color of the graphed function and reset the graph to its default view using the 'home' button is discussed. Additionally, the presenter explains how to adjust the graph's appearance by modifying grid lines and axis steps, which can help in better visualizing the graph.
🔍 Advanced Desmos Features and Troubleshooting
This section delves into more advanced features of Desmos, such as the ability to graph equations that don't immediately display by removing the 'equals zero' at the end. The presenter then uses Desmos to solve a problem where a line intersects a parabola at exactly one point, illustrating how to adjust the value of 'C' using a slider to find the intersection. The video also addresses how to handle errors in Desmos, such as when an equation doesn't graph correctly, and suggests solutions like adding '+0x' to make the equation implicit in 'x'.
🧩 Using Desmos to Solve SAT Problems
The presenter uses Desmos to solve a specific SAT problem involving a parabola and a line intersecting at a single point. By graphing the parabola and adjusting the line's equation with a slider, the video shows how to find the exact value of 'C' that results in the desired intersection. The process highlights the utility of Desmos for quickly solving complex problems that might be time-consuming to solve algebraically. The video also touches on the importance of careful reading of the problem and selecting the correct variable to find the solution.
📚 Desmos in SAT Practice and Additional Problem Types
The final part of the video covers the use of Desmos for solving a variety of SAT problems, including those involving quadratics and systems of equations. The presenter demonstrates how to adjust sliders to find values that result in a graph with more than one real solution, showcasing Desmos's efficiency in solving such problems. The video concludes with a brief mention of other types of problems that can be solved using Desmos, like simple linear equations, emphasizing the tool's versatility. The presenter encourages viewers to practice using Desmos and offers resources for further study.
Mindmap
Keywords
💡Desmos
💡Graphing Calculator
💡SAT
💡Function
💡Exponent
💡Parabola
💡Slider
💡X-intercept
💡Discriminant
💡Vertex
Highlights
Desmos is a graphing calculator that can be used to assist with SAT questions.
Access Desmos at desmos.com or by searching for 'Desmos calculator'.
Desmos allows you to graph equations by simply typing them in.
Use the shift key and a number to input exponents in Desmos.
Desmos automatically graphs new functions in different colors.
Click the gear icon to change the color of a graphed function.
Use the home button to reset the graph to its default zoom.
Desmos settings can be adjusted to show or hide grid lines.
Manually adjust the x-axis and y-axis ranges using the settings.
Changing the axis step can help see all the numbers on the graph.
Desmos may not graph equations with 'equals zero' at the end; try removing it.
Desmos can solve for the value of C in an equation where a line intersects a parabola at exactly one point.
Use the keypad in Desmos for easier input of numbers and functions.
Desmos offers a slider feature to adjust the value of a variable and see its effect on the graph.
Adjust the slider range and step to find the exact value where two graphs intersect at one point.
Desmos can be used to solve quadratic equations and find x-intercepts.
For equations that may not graph correctly, try adjusting the equation format in Desmos.
Desmos can quickly show the solution to an equation by graphing it and finding the x-intercept.
Use Desmos for a variety of SAT question types, including systems of equations and quadratics.
Desmos can simplify solving equations by visually representing where lines intersect on a graph.