Hi Everyone!
On this page you will find some material about Lesson 10. Read through the material below, watch the videos, and follow up with your instructor if you have questions.
Lesson 10: Graphs of Quadratic Expression, Vertex Formula and Standard Form
Table of Contents
Resources
In this section you will find some important information about the specific resources related to this lesson:
- the learning outcomes,
- the section in the textbook,
- the WeBWorK homework sets,
- a link to the pdf of the lesson notes,
- a link to a video lesson.
Learning Outcomes.
- Identify the concavity of the parabola by analyzing the quadratic expression.
- Find the
- and -intercepts of a quadratic function. - Find the vertex of a parabola by completing the square and by using the vertex formula.
- Find the equation of the axis of symmetry.
- Graph a parabola by labeling the
- and -intercepts, the vertex and the axis of symmetry.
Topic. This lesson covers
Section 7.4: Graphs of Quadratic Functions, and
Section 7.5: Vertex of a Parabola.
WeBWorK. There are four WeBWorK assignment on todayβs material:
ShiftingParabolas
ParabolaLab
ParabolaVertices-CtS
ParabolaVertices-VertexFormula
Lesson Notes.
Video Lessons.
Video Lesson 13 β part 1 (based on Lesson 13 Notes β part 1)
Video Lesson 13 β part 2 (based on Lesson 13 Notes β part 2)
Warmup Questions
These are questions on fundamental concepts that you need to know before you can embark on this lesson. Donβt skip them! Take your time to do them, and check your answer by clicking on the βShow Answerβ tab.
Review
If you are not comfortable with the Warmup Questions, donβt 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 thatβs perfectly fine.
Need a review? Check
Quick Intro
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 β 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 Graphs of Quadratic Functions & Vertex of a Parabola
Key Words. Quadratic function, graph, parabola,
The graph of a quadratic function
is a parabola. The graph below shows three parabolas.
From left to right:
- Parabola 1 (in red): concave down, intersects the
-axis at two points. - Parabola 2 (in blue): concave up, intersects the
-axis at one point only. - Parabola 3 (in orange): concave up, does not intersect the
-axis.
When graphing a quadratic function
The number of
The
- By completing the square, we can rewrite
as In this case, is the vertex.
- By using the vertex formula, the vertex is
Video Lesson
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 β starting from a simple one to a more complex one. Feel free to play them as many times as you need. Pause, rewind, replay, stopβ¦ follow your pace!
Video Lesson
A description of the video
- Find the
- and -intercepts, the vertex and the graph of the parabola . - Find the
- and -intercepts, the vertex and the graph of the parabola .
Try Questions
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 βShow answerβ tab to see if you got the correct answer.
WeBWorK
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.
WeBWork
It is time to do the homework on WeBWork:
ShiftingParabolas
ParabolaLab
ParabolaVertices-CtS
ParabolaVertices-VertexFormula
When you are done, come back to this page for the Exit Questions.
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 βShow Answerβ tab is there for you to check your work!
Need more help?
Donβt wait too long to do the following.
- Watch the additional video resources.
- Talk to your instructor.
- Form a study group.
- Visit a tutor. For more information, check the tutoring page.