Lesson 1 ET on the Run Develop Understanding
Learning Focus
Model patterns with functions.
Compare and contrast linear and quadratic functions.
How can I use representations to model a growing pattern?
What kind of function is the sum of a linear and quadratic function?
Open Up the Math: Launch, Explore, Discuss
DeShawn is designing an old-school style video game featuring extraterrestrials invading the earth. He has created the following set of images for his program:
1.
Assuming the pattern continues to grow in the same way, use a table, graph, and equation to model the number of unshaded blocks that make up the eyes, arms, and legs in each image.
2.
Is the model you made in problem 1 a function? Why or why not?
3.
If the model you made in problem 1 is a function, what type of function is it? Explain.
4.
For a given image, model the number of blocks in the shaded area that make up the body of the space creature using a table, graph, and equation.
5.
What type of function is your model for the number of blocks in the body? How do you know?
6.
Now, model the total number of blocks in the given image with a table, graph, and equation.
7.
Which representation did you find first, and how did you use your previous work to find it?
8.
What type of function is the model for the total number of blocks? How do you know?
9.
Examine the equations for each of the three models you have created. What relationships do you see?
10.
Examine the graphs for each of the three models you have created. What relationship do you see?
Ready for More?
Find a second way to annotate the diagram and write an equation. Then, verify that your new equation is equivalent to your original equation
Takeaways
Linear | Quadratic | Linear + Quadratic | |
|---|---|---|---|
Diagram | |||
Equation | |||
Table | |||
Rate of change | |||
Graph |
Vocabulary
- linear function
- parabola
- quadratic function
- Bold terms are new in this lesson.
Lesson Summary
In this lesson, we modeled a quadratic and a linear function and compared representations. We combined a linear function and a quadratic function to examine the representations of the combined function. We noticed that when two functions are added, their corresponding outputs are added to make the new function.
Draw an area model to represent each set of factors. Then. multiply each set of factors and provide the equivalent expression in standard form.
1.
Standard Form:
2.
Standard Form:
Identify the functions in the tables as linear, exponential, quadratic, or neither.