On this page you will find some material about Lesson 12. Read through the material below, watch the videos, and follow up with your instructor if you have questions.
Lesson 12: Applications of Quadratic Equations
- Apply knowledge of algebra to solve verbal problems
Topic. This lesson covers
Section 4.8.2: Applications of Quadratic Equations, and
Section 7.2.3: Using the Quadratic Formula in Applications.
WeBWorK. There is no WeBWorK assignment on today’s material.
Video Lesson 12 – part 1 (based on Lesson 12 Notes)
Video Lesson 12 – part 2 (based on Lesson 12 Notes)
These are questions on fundamental concepts that you need to know before you can embark on this lesson. Don’t skip them! Take your time to do them, and check your answer by clicking on the “Show Answer” tab.
If you are not comfortable with the Warmup Questions, don’t give up! Click on the indicated lesson for a quick catchup. A brief review will help you boost your confidence to start the new lesson, and that’s perfectly fine.
This is like a mini-lesson with an overview of the main objects of study. It will often contain a list of key words, definitions and properties – all that is new in this lesson. We will use this opportunity to make connections with other concepts. It can be also used as a review of the lesson.
A Quick Intro to Applications of Quadratic Equations
Key Words. Quadratic equations, applications.
Here are some suggestions when solving a verbal problem.
- Read the problem several times.
- Identify what the question is asking for. That is the unknown.
- Write down the information that is given.
- Draw a picture.
- Find relationships.
- Is the problem related to areas, volumes etc? Is it about a square, rectangle, circle etc? Write down the related formula.
- Plug all the pieces of information that are given.
- Identify the equation you need to solve.
- Solve and check.
Recall that we have seen three methods for solving a quadratic equation.
- Factor and use the Zero Product Rule
- Use the Square Root Property; complete the square first, if necessary
- Use the Quadratic Formula
Do you know when to use each method?
Many times the mini-lesson will not be enough for you to start working on the problems. You need to see someone explaining the material to you. In the video you will find a variety of examples, solved step-by-step – starting from a simple one to a more complex one. Feel free to play them as many times as you need. Pause, rewind, replay, stop… follow your pace!
Video Lesson 1
A description of the video
In the video you will see the following problems.
- Suppose you have a 100 ft of fencing to make a rectangular enclosure, using a house as one side. Suppose you want the area to be 1200 . What are the dimensions of the enclosure?
- Suppose in the above example, the area is 100 .
- Try: suppose area is 5000 sqft. What are the dimensions of the enclosure then?
Video Lesson 2
A description of the video
In this video you will see the following problem.
- Suppose Tasha throws a ball in the air and suppose the height in feet of the ball in terms of time in seconds.
Now that you have read the material and watched the video, it is your turn to put in practice what you have learned. We encourage you to try the Try Questions on your own. When you are done, click on the “Show answer” tab to see if you got the correct answer.
You should now be ready to start working on the WeBWorK problems. Doing the homework is an essential part of learning. It will help you practice the lesson and reinforce your knowledge.
There is no WeBWorK assignment on today’s material, but you can do the homework from the textbook.
When you are done, come back to this page for the Exit Questions.
After doing the WeBWorK problems, come back to this page. The Exit Questions include vocabulary checking and conceptual questions. Knowing the vocabulary accurately is important for us to communicate. You will also find one last problem. All these questions will give you an idea as to whether or not you have mastered the material. Remember: the “Show Answer” tab is there for you to check your work!
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