Vertex form of a Quadratic Model: f(x) = a(x − h)2  + k

1 Does it make sense for a to be negative or positive for this curve?

Why

2 Estimate h (the x-coordinate of the vertex of this dataset):

3 What y-coordinate of the vertex ( k ) would best match the shape of the curve?

Fitting the Model Visually in Desmos

For this section, open Exploring Quadratic Functions(Desmos) to Slide 8: Fitting a Model: Bat Angle v Hit Distance (Full Data).

4 Using what you know about the values of a, h, and k, adjust the sliders to fit a quadratic model to the data. Continue adjusting the sliders until you’ve landed on the best model you can. Record your values for a, h, and k below.

a: h: k:

5 Using the values of a, h, and k you decided on in the Desmos file, define your quadratic function below in Pyret notation.

fun judge(x) : end

6 Which subset of the data appears to be visually the most similar to the full dataset?

7 What does that mean

You could have students make count(judge-table, "pitch-type") to have something more concrete to discuss.

Testing how Good the Model is in Pyret

Open your copy of the Aaron Judge Starter File. Adjust the definition for judge(x) on line 54 and click "Run".

8 Use fit-model to fit your function to the data in the judge-table. What S-value did you get?

What does this model actually mean?

After experimenting, I came up with a quadratic model for this dataset showing that x-variable is correlated to y-variable.

The error in the model is described by an S-value of about Sunits. I strongly agree, agree, disagree, strongly disagree that this model is a good fit considering that y-variable in this dataset range from lowest y-value to highest y-value.

The vertex of the parabola drawn by this model is a minima or maxima? at about (x, y), which means that

Before this point, as bat angle increases, hit distance . After this point, as the angle increases hit distance

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.