Learning Resources
Lesson
As a quick review for this Focus, graph
Answer the following questions with respect to your equation and graph
- Does the graph have a minimum or maximum y-value ? How do you know?
- Does the graph open upward or downward ?
- How does the shape of the graph compare to
? - Where is the location of the line or axis of symmetry ? How do you know ?
- Where is the location of the the y-intercept ? x-intercepts ? How easy is it to find them ?
- Where is the location of the vertex ?
To check your memory click here.
Have you completed the review exercise ? If so continue with the lesson.
Read and study Focus C (p.24 - 30) with particular emphasis on the examples used. Make sure that you write complete answers in your notebook for the questions accompanying each example. You should find the similarities and differences for the standard form and the general form of the quadratic. Pay particular attention to the significance of the a in both forms of the equation and the c in the general form.
As you progress through the Focus you will note the usual transformation techniques being used to graph the equations; however, pay particular note to the method of graphing the vertical stretch for the graphs. Follow the steps by clicking on the Go forward one frame button below. Read and follow each step to see an illustration of how the vertical stretch can be graphed for parabolas.
It does not matter where the parabola is located in the plane, starting with the vertex and using the vertical stretch you can find the points to graph it; remember that the parabolas are symmetric and other points can be found on the other side of the line of symmetry to correspond to the those graphed.
After having studied the Focus, answer the Focus Questions from the activities list.
If you are having any problems or concerns with this focus continue to the next page for some hints and clues to help you.
Each example in the Focus looks at how the graph of is transformed by various equations and leads you to describing it in standard form and general form. It is important for you to see how 
is converted to 
.
Follow the steps by clicking on the Go forward one frame button below. Read and follow each step:
For 
, then a = 2, b = 0 ( Since there is no linear term ) and c = 1
Look at the graph and find the significance of the 2 and the 1.
In Example 3, the equation is changed as follows:
Follow the steps by clicking on the Go forward one frame button below. Read and follow each step:
This gives standard form for the equation . To obtain the general form continue as follows:
Follow the steps by clicking on the Go forward one frame button below. Read and follow each step:
For , 
, b = -2 and c = 1 . Again note the significance of the 
and the 1 on the given graph.
Activity
Focus Questions p.29 - 30. Complete 1, 2, 3, 4 and 5
Think About p24, p.26, p.28 and p.30
Challenge Yourself p.30
Check Your Understanding p.30 - 31. Complete #6 to 13 inclusive
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
After you do the assigned activities, continue on to the Test Yourself section below for a quick quiz on this lesson.
Test Yourself
Write a Journal entry in which you discuss the advantages and disadvantage for each of the forms of the quadratic equation.
Questions:
1. Use the mapping rule 
to write all three forms of the quadratic function
2. Given that (2, -1) is the vertex for a family of parabola, create the function which will describe all these parabolas. Express it in all three forms.
Check your solutions.