Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 46518
Graphing Quadratics Made Easy: Vertex Form of the
Equation
This lesson covers quadratic translations as they relate to vertex form of a quadratic equation. Students will predict what will happen to the graph of
a quadratic function when more than one constant is in a quadratic equation. Then, the students will graph quadratic equations in vertex form using
their knowledge of the translations of a quadratic function, as well as describe the translations that occur. Students will also identify the parent
function of any quadratic function as
.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Instructional Time: 50 Minute(s)
Freely Available: Yes
Keywords: quadratic functions, graphing quadratic functions, vertex form, function translations
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Translating Quadratic Functions in VertexForm.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will identify the parent function of a quadratic function as
.
Students will explain the translation of the graph of a quadratic function, given the vertex form of the function.
Students will graph quadratic functions given the vertex form of the equation.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students will need to know how each of the following transformations affects the graph of the parent function,
:
1.
2.
3.
Students will need to know that the graph of a quadratic function is a parabola, as well as the features of a parabola (max/min point, vertex, axis of symmetry).
Guiding Questions: What are the guiding questions for this lesson?
How can the vertex form of a quadratic function help me graph that function?
What information about a quadratic function can I get by looking at the equation in vertex form?
Teaching Phase: How will the teacher present the concept or skill to students?
page 1 of 4 1. Complete the "Commit and Toss" activity detailed in the Formative Assessment box. Teacher will explain that
is an example of the vertex form of a quadratic function and how to graph a parabola
using that form:
2. Display the equation
, and explain to students that
this is the general vertex form of a quadratic function.
3. Explain that the parent function (or the "normal quadratic function") is
, and that the a, h, and k in the
vertex form translate that graph around the coordinate grid.
4. Explain that the vertex of the parabola comes from an equation of that form and is
.
5. Explain that h is also the horizontal shift of the parabola, and k is the vertical shift of the parabola. It is also where the axis of symmetry is, and x=h is the equation
of the axis of symmetry.
6. Explain that a determines two things: the stretch of the parabola and how the parabola opens. The sign of a determines the opening (+ opens up, - opens down),
and the magnitude of
determines the stretch (If
, the parabola will be more narrow/stretch up, if
, the parabola will be wider/stretch out). Also, if
point at the vertex, and if
, the parabola will have a minimum
, the parabola will have a maximum point at the vertex.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Work through graphing these functions and describing the transformations of the parent function with the students:
1.
(The 3 will translate the graph to the right 3 units, the 5 will translate the graph up 5 units, and the 1/2 will stretch the graph horizontally/made it wider).
2.
(The 1 will move the graph to the left 1 unit, the -2 will move the graph down 2 units, and the -3 will stretch the graph vertical/make it more narrow and will open
down)
***Complete the "Independent Practice" section next, then the "Closure" activity.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Teacher will assign 6 quadratic functions to graph and describe the transformations of the parent function (see attached worksheet). Work is to be done individually,
where students can raise their hand and ask a question of the teacher if needed.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
***Complete the Independent Practice section before completing the Closure.
1. Teacher will choose six students to display their work to the class (either using a document camera one at a time, writing all of their answers up on the board, or
any other available method).
2. As each student shares their answer, teacher will select two students to share why they agree with the work and two students to share why they disagree (if any).
3. Class will continue to discuss each graph until everyone agrees with the graph displayed (should be the correct answer).
Summative Assessment
Students will be assessed based on the information presented in the closing discussion. Here is a checklist of information students should know:
Can students identify the parent function of a quadratic function?
Given a quadratic equation in vertex form, can students explain the translations that occur?
Given a quadratic equation in vertex form, can students identify the vertex of the parabola?
Given a quadratic equation in vertex form, can students graph the parabola defined in the equation?
Formative Assessment
Formative assessment will occur during the introduction to the lesson in listening to the responses to the "Commit and Toss" activity. It will also occur during the
guided practice, as the teacher leads students through the two examples.
Directions for "Commit and Toss" activity:
1. Display this function:
and ask
students to think about what effect each number might have on the graph of a quadratic function.
2. Students will write down their ideas on a half-sheet of paper.
3. Then, students will crumple up their paper. (This activity is called "Commit and Toss")
page 2 of 4 4. Have the students stand up and throw their paper balls around the room (can do just one throw or multiple throws, depending on the behavior of your students).
5. Next, students will pick up a paper ball closest to them, open it up, and remain standing.
6. Ask for a student volunteer to read what's written on their paper, reminding them that it isn't their answer so no one will be judging them.
7. Once a student has read their ideas, tell other students to sit down if their paper said the same thing (or something really close).
8. Continue reading responses until all students are seated.
Feedback to Students
-Students will receive direct and indirect feedback on their work during the closing of the lesson. During the discussion, students will be able to see if their answers
were correct, as well as where they may have gotten confused.
-Feedback can also be provided during the independent practice session. The teacher can circulate the room and provide feedback to students as they work on the
independent practice problems.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Provide a fill-in-the-blank notes sheet with grids available for graphing.
Students could work with a partner or in groups during the independent practice time.
Students could graph the equations using a graphing calculator in order to describe the translations that occur.
This is not a comprehensive list of accommodations. Be sure to consult a student's IEP and/or 504 plan for more individualized accommodations.
Extensions:
Illustrative Mathematics Task #388 would be a significant extension after students have mastered the vertex form of the parabola.
388.pdf
Source: Illustrative Mathematics
Special Materials Needed:
Half-sheets of paper for students to complete the "Commit and Toss" activity (could be teacher-provided or student-provided)
Could need graphing calculators for accommodating students
Further Recommendations:
Be sure to follow the outline in this order when teaching the lesson:
1. Teaching Phase
2. Guided Practice
3. Independent Practice
4. Closure
Additional Information/Instructions
By Author/Submitter
This lesson should be used after "Translating Quadratic Functions," or after students understand the effect of one constant on the graph of a quadratic functions.
This lesson may align with the following standards of math practice:
MAFS.K12.MP.5.1 - Use appropriate tools strategically. (Reason - Students may choose to graph using pencil-and-paper, graphing calculator, or other technology.)
MAFS.K12.MP.6.1 - Attend to precision. (Reason - Graphing equations inherently requires precise understanding of mathematical notation and how to interpret the terms of
the vertex form of the parabola.)
SOURCE AND ACCESS INFORMATION
Contributed by: Amy Herring
Name of Author/Source: Amy Herring
District/Organization of Contributor(s): Volusia
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases. ★
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
page 3 of 4 MAFS.912.F-IF.3.7:
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value
functions.
c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing
end behavior.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions,
showing period, midline, and amplitude, and using phase shift.
page 4 of 4