Lesson Title: A.SSE.2 Rewriting Quadratic Equations in Different Forms Course: Algebra I, Unit 4
Date: _____________ Teacher(s): ____________________
Start/end times: __________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
Lesson Launch Notes: Exactly how will you use the
Lesson Closure Notes: Exactly what summary activity,
first five minutes of the lesson?
questions, and discussion will close the lesson and provide
Tell as much as you can about the graph of each
a foreshadowing of tomorrow? List the questions.
function without graphing on your calculator or
The function h(t) describes the height (h) of a football t
rewriting the equation.
seconds after it is punted. Tell which form of the equation
1. f(x)=-2(x – 3)2 + 5
you would need to answer the following questions:
2. g(x) = 4(x + 1)(x – 7)
 How high did the ball go?
3. h(x) = 6x2 - x - 2
 When did the ball land?
 What was the height of the ball when it was
kicked?
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
1. Following the discussion on the graphical characteristics of the warm-up functions, ask students to rewrite f(x) in
standard form, g(x) in standard form, and h(x) in factored and vertex form. Students may struggle with rewriting
the functions. Explain how each form might be manipulated to arrive at another form. Encourage students to
find the vertex of h(x) on the calculator and substitute the coordinates for h and k, as opposed to completing the
square. Ask the students what additional information they can determine about each graph after rewriting the
equation.
Investigation (Adapted from Discovering Advanced Algebra*)
2. Set up the investigation and have students work through the investigation. (Note: A station could be set up for
each group to collect their own data, groups could take turns collecting data from a single station, or one set of
data could be used for the whole class.)
a. Prop up the end of a table slightly and place the motion sensor at the low end. Mark a starting line 0.5 m
from the sensor with chalk or tape.
b. Have students roll the can up the table directly in front of the motion sensor starting behind the starting
line. Give the can a gentle push so that it rolls up the table, stops near the end of the table, and then rolls
back. Catch the can after it crosses the line and before it hits the motion sensor.
c. Set the calculator to collect data for 6 seconds. The data collected will be collected as time versus
distance, but you should discuss adjusting for the distance between the starting line and sensor by
subtracting 0.5 from each y-value.
d. Students will work in groups to analyze the data, letting x represent the time in seconds and y represent
the distance from the line in meters. (Note: Students may choose to do this by plotting their data on
graph paper, creating a graph on the calculator, or using a table of data to estimate the vertex and xintercepts.)
3. Have students use their data to write a quadratic equation in vertex form y = a(x – h)2 + k.
4. Have students use their data to write a quadratic equation in factored form y = a(x – r1)(x – r2) where r1 and r2 are
the zeros.
5. Students will verify that the two equations are the same graphically and algebraically. If the groups’ two
equations are not equivalent, students should revisit the data to revise their equations. Teachers may need to use
guiding questions to direct their process.
Part III – Discussion
6. When student groups have each completed the investigation, bring students together for a whole class
discussion. Ask students:
 What are the three forms of quadratic equations?
 What is the purpose for having three forms?
 What did you notice about the values of a in each form?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: A.SSE.2 Rewriting Quadratic Equations in Different Forms Course: Algebra I, Unit 4
Date: _____________ Teacher(s): ____________________
Start/end times: __________
 How do the different values in each form relate to the rolling can? Vertex is maximum distance from the line
and the zeros are when the can crosses the starting line.
 Why were the y-values repeated in the data set? Relate this to the symmetry of quadratic functions.
 Why was each group’s equation different? What things affected the shape of the graph or the equation?
7. Give half the students a different vertex form equation and the other half an equivalent factored from equation.
Have students individually convert the equation to standard form and then find their partners. In pairs, the
students will produce a graph based on the information they have from the three forms.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students will recognize the different forms of quadratic equations (standard, vertex, and factored forms) and identify
the graphical features that each form provides. Students will rewrite each form into an alternate form to identify
other graphical features. Evidence of success will be measured during student participation during the group activity
and successful completion of the closure activity.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Students may require additional practice on rewriting equations before the investigation.
Students should not be expected to rewrite standard form equations in vertex form using completing the square. This
is a standard that will be taught later in the unit.
Students may struggle with determining the a-value for the vertex and factored forms. Suggest putting in the known
values (zeros, or vertex coordinates) and then selecting.
Teachers can modify the investigation by having two students demonstrate and collect data for the whole class.
If 6 seconds is not long enough, students can adjust the time. The student who is rolling the can should wait until the
motion sensor starts checking before rolling the can.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Motion Sensor/CBR
Cans (empty)
Books (to raise one side of table)
Graph Paper
Graphing Calculators
Create a summary that demonstrates how to rewrite vertex
form in standard form, rewrite factored form in standard
form, and rewrite standard form in factored form. Include
the benefits for each form in your summary. Choose a
pamphlet, poster, or PowerPoint presentation.
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?
Can students rewrite vertex form equations to standard form? Factored form to vertex form? Standard form to
factored form?
Can students determine which form is necessary to find certain graphical features/behaviors?
*
Jerald Murdock, Ellen Kamischke, & Eric Kamischke. (2010) Discovering Advanced Algebra.
Emoryville, CA: Key Curriculum Press.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.