In this activity, you will solve a case problem that requires them to find the dimensions of r and x that yield the athletic field with the greatest possible area.

Step 1. Review

Review the learning resources for this lesson before studying the case problem.

Step 2. Analyze

Analyze the case problem below.

Step 3. Respond

Respond to the case problem by finding the dimensions of r and x that yield the athletic field with the greatest possible area. Include the following:

• Complete calculations
• Justifications such as  theorems, properties, or laws
• Any other components you used that enabled you to move from one step to another.

Step 4. Share

To share your work, click on the “Add new discussion topic” button under this post and paste your work in the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

Step 5: Interact

OPTIONAL Step 6: Interact (10 minutes)

If you would like to, you can reply to your peers' posts in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to forum.”

In this activity, you will explore a virtual quadratic function explorer and answer succeeding questions about its different features.

Step 1. Explore 

Explore this virtual quadratic function explorer here http://www.mathopenref.com/quadraticexplorer.html

Step 2. Manipulate

Manipulate the function explorer by initially clicking the word “zero” under all three sliders. The “a”, “b”, and “c” correspond to the coefficients a, b, and c in a quadratic equation used in the quadratic formula. Then, follow these steps:

1. Move the slider “a” up and down.  Observe what happens to the quadratic function when:

2. Put the “a” slider at 1, the “c” slider at zero. We are now going to move the “b” slider.  Observe what happens to the quadratic function when:

3. Put the “a” slider at 1, the “b” slider at zero. We are now going to move the “c” slider.  Observe what happens to the quadratic function when:

4. Now you are going to look at the function with a moving vertex. Click on the words “Quadratic Explorer – Standard Form”. This should change to the Vertex form.

5. Put the “a” slider to a = 1, and the “k” slider to k = 0. We will move the “h” slider.

6. Put the “a” slider to a = 1, and the “h” slider to h = 0. We will move the “k” slider.

7. We are moving both the “h” and the “k” sliders.

               Generalize what happens when you move both the “h” and the “k” sliders.

8.   Graph a quadratic function with h and k.

Fill out the table, plot the points and graph the function.

Step 3. Respond

Respond to this lab activity by putting all to writing all observations and descriptions from items #1-7. For item # 8, fill in the table, plot the points and finally graph the function.

Step 4. Share

To share your work, click on the “Add a new discussion topic” button under this post and paste your work in the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

Step 5: Interact

OPTIONAL Step 6: Interact (10 minutes)

If you would like to, you can reply to your peers' posts in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to forum.”