Lesson 7
1. Lesson 7
1.4. Discover
Module 3: Quadratics
Discover
Try This 1 gives you a chance to play with the factored form of the quadratic function. The activity will let you see how the various parameters affect the shape of the function’s graph.
Try This 1
Use Polynomial Function Explorer to explore the factored form of the quadratic equation. Change the “Degree =” slider to 2 so you get a second-degree polynomial—a quadratic function. Choose “Show x-intercepts” by clicking on the square. Experiment with the b-slider to see how the slider changes the values in the factored form of the function, the intercepts, and the position of the graph.
- When you are satisfied that you know what the b-slider does and how changing the value affects the graph, set the value of b to 4. Experiment with the k-slider to see how the value of k changes the function, the intercepts, and the position of the graph. How many different graphs are possible that have x-intercepts of 1 and 4?
- If you put k = 2, the graph passes through (5, 8). Can you make another graph with the x-intercepts of 1 and 4 that passes through (5, 8)? Move the k-slider and see if you can find one. What can you conclude about a graph where the x-intercepts and one other point are defined?
Share 1
Submit your work for Share 1 to your teacher for marking.
Based on your observations using Polynomial Function Explorer, discuss the following questions with another student or appropriate partner.
- How many functions can have exactly the same x-intercepts?
- One way to specify a particular function is to give the constants in the formula, such as f(x) = 2(x − 1)(x − 4). What is another way involving the x-intercepts?
Summarize your discussion by creating a short paragraph describing the answers to the questions that you and your partner agreed upon. (4 marks)
Place a copy of this in your course folder for reference later in the course.