Fitting the Model Visually 𝑓(𝑥) = 𝑎(𝑥 - 𝒽)2 + 𝑘

For this section, you’ll need to have Slide 1: Quadratic Model for MA of Modeling Covid Spread (Desmos) open on your computer.

1 Try changing the values of 𝑎, 𝒽 and 𝑘 to find three promising quadratic models, graphing each one and labeling your values in the grids below.

𝑎 =
𝒽 =
𝑘 =

𝑎 =
𝒽 =
𝑘 =

𝑎 =
𝒽 =
𝑘 =

2 Do your quadratic models open up or down? Up. What does that tell us about 𝑎? It’s positive.

3 Describe one of your models: Where is the vertex? (x, y) What is the horizontal shift? 𝒽 The vertical shift? 𝑘

4 Which quadratic form would be the easiest to fit to this data? standard ☐ factored ☐ vertex☐

Fitting the Model Programmatically 𝑓(𝑥) = 𝑎(𝑥 - 𝒽)2 + 𝑘

For this section, open your copy of the Covid Spread Starter File.

5 In the space below, define quadratic1 to be the first model you fit in Desmos.

fun quadratic1(x): ( a * (num-sqr( x - h ))) + k end

6 Return to Covid Spread Starter File and update the definitions for quadratic1, quadratic2, and quadratic3.
Then click "Run" to load your updated definition.

7 Use fit-model to determine the 𝑆-value of each model using the MA-table.

Hint: If you forgot the contract for fit-model, look it up in the contracts pages!

𝑆 for quadratic1: 𝑆 for quadratic2: 𝑆 for quadratic3:

What does this model actually mean?

Numerical values below will vary!

After experimenting, the best quadratic model I came up with for this dataset shows that x-variable are correlated to y-variable.
The vertex of the parabola drawn by this model is a minima or maxima? at about (x, y), which predicts that .
The error in the model is described by an S-value of about Sunits, which is a bad, ok, good
fit considering that y-variable in this dataset range from lowest y-value to highest y-value.

Are Quadratic Models a Good Fit for This Data?

8 Would you feel good about making predictions based on these models? Why or why not?

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). CCbadge Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.