Lesson 4 Transformers: Shifty y’s Develop Understanding
Find patterns in the equations and graphs of quadratic functions.
What happens to the graph of
Open Up the Math: Launch, Explore, Discuss
Optima Prime is designing a robot quilt for her new grandson. She plans for the robot to have a square face. The amount of fabric that she needs for the face will depend on the area of the face, so Optima decides to model the area of the robot’s face mathematically. She knows that the area
What is the domain of the function
Match each statement about the area to the function that models it.
The length of each side is increased by
The length of each side is multiplied by
The area of a square is increased by
The area of a square is multiplied by
Optima started thinking about the graph of
Optima began wondering about how changes to the equation of the function, like adding
Make your own predictions of how the graphs of each of the following equations will be the same or different from the graph of
Similarities to the graph of
Differences from the graph of
Optima decided to test her ideas using technology. She thinks that it is always a good idea to start simple, so she decides to go with
Knowing that things make a lot more sense with more representations, Optima tries a few more examples, like
After her amazing success with addition in the last problem, Optima decided to look at what happens with addition and subtraction inside the parentheses, or as she says it, “Adding to the
Optima thought that problem 7 was very tricky and had hoped that multiplication was going to be more straightforward. She decides to start simple and multiply by
Optima is encouraged because she was able to figure out the last problem. She decides to end her investigation for the day by determining the effect of a multiplier,
Ready for More?
Use technology to explore the behavior of the line
In this lesson, we explored transformations of the function
Draw a line of symmetry for the graph, state whether the graph has a maximum point or a minimum point, and provide the coordinates for that point.
Graph the linear equations, and explain your strategy.