How to Determine the Quadratic Equation of a Given Table (with three points) Using Desmos

Introduction

This tutorial will guide you through the process of determining the quadratic equation of a given table containing three points, using Desmos. Quadratic equations take the form (y = ax^2 + bx + c), and knowing how to derive these equations is essential for various applications in algebra and data analysis.

Step 1: Gather Your Data Points

Before starting with Desmos, you need to have three distinct points from your table. Each point should be in the format (x, y).

• Example points could be:
  • Point 1: (1, 2)
  • Point 2: (2, 5)
  • Point 3: (3, 10)

Step 2: Input Data Points into Desmos

1. Open Desmos in your web browser.
2. In the input area, enter each data point in the following format:
   • (1, 2)
   • (2, 5)
   • (3, 10)

This will plot your points on the graph.

Step 3: Create the Quadratic Function

1. To find the quadratic equation, you need to define a general quadratic function in Desmos:
   • Type y = a*x^2 + b*x + c in the input area.
2. Desmos will create sliders for the coefficients (a), (b), and (c).

Step 4: Adjust the Sliders to Fit the Points

1. Use the sliders to adjust the values of (a), (b), and (c) until the curve passes through all three points.
2. Observe how the graph changes as you manipulate the sliders.

Practical Tip

• Start with smaller adjustments to the sliders and gradually refine your values.

Step 5: Verify the Equation

1. Once you have a curve that fits through the three points, note the values of (a), (b), and (c) from the sliders.
2. Write down the quadratic equation in the form:
   • (y = ax^2 + bx + c)

Common Pitfalls to Avoid

• Ensure that your three points are not collinear (i.e., they do not lie on a straight line) since this would not yield a valid quadratic equation.
• Double-check the accuracy of your points to ensure they are correctly plotted.

Conclusion

In this tutorial, you've learned how to determine the quadratic equation from a set of three points using Desmos. By following these steps, you can effectively model relationships using quadratic functions. Next, you can explore more complex data sets or try deriving equations from different types of functions to enhance your understanding of mathematical modeling.