Curriculum / Math / 9th Grade / Unit 7: Quadratic Functions and Solutions / Lesson 8
Math
Unit 7
9th Grade
Lesson 8 of 13
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Lesson Notes
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Factor special cases of quadratic equations—difference of two squares.
The core standards covered in this lesson
A.SSE.A.1.A — Interpret parts of an expression, such as terms, factors, and coefficients.
A.SSE.A.2 — Use the structure of an expression to identify ways to rewrite it. For example, see x<sup>4</sup> — y<sup>4</sup> as (x²)² — (y²)², thus recognizing it as a difference of squares that can be factored as (x² — y²)(x² + y²).
A.SSE.B.3.A — Factor a quadratic expression to reveal the zeros of the function it defines.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Lessons 8 and 9 look at specific cases of factoring quadratic expressions—difference of two squares and perfect square trinomials. Depending on the needs of your students, these lessons can be kept separate or combined together. These lessons are also a good opportunity to spiral in other factoring problems from Lessons 4–7.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Aaron says that when you multiply two linear binomials, you will always get a trinomial. Alison disagrees and finds an example where two linear binomials multiplied together produce a quadratic binomial.
Find an example that demonstrates Alison’s claim is true.
Find the solutions to the quadratic equations below.
a. $${y=x^2-196}$$
b. $${y=16x^2-121}$$
c. $${y=75x^2-27Â }$$
Graphs of two quadratic functions are shown below.
Which graph represents a quadratic function whose equation is a difference of two squares? Explain how you know.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Factor each expression completely.
a.  $${x^2-36}$$
b.  $${12x^2-3}$$
c.  $${6x^2+34x-12}$$
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Factor special cases of quadratic equations—perfect square trinomials.
Topic A: Features of Quadratic Functions
Compare quadratic, exponential, and linear functions represented as graphs, tables, and equations.
Standards
F.IF.B.4F.LE.A.2
Identify key features of a quadratic function represented graphically. Graph a quadratic function from a table of values.
F.IF.B.4F.IF.C.7.A
Calculate and compare the average rate of change for linear, exponential, and quadratic functions.
F.IF.B.4F.IF.B.6F.LE.A.3
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Topic B: Factoring and Solutions of Quadratic Equations
Factor quadratic expressions using the greatest common factor. Demonstrate equivalence between expressions by multiplying polynomials.
A.APR.A.1A.SSE.A.2A.SSE.B.3.A
Identify solutions to quadratic equations using the zero product property (equations written in intercept form).
A.APR.B.3F.IF.C.8.A
Factor quadratic equations and identify solutions (when leading coefficient is equal to 1).
A.SSE.A.1.AA.SSE.B.3.A
Factor quadratic equations and identify solutions (when leading coefficient does not equal 1).
A.SSE.A.1.AA.SSE.A.2A.SSE.B.3.A
A.SSE.A.2A.SSE.B.3.A
Solve quadratic equations by factoring. Compare solutions in different representations (graph, equation, and table).
A.SSE.B.3.AF.IF.C.8.AF.IF.C.9
Solve quadratic equations by taking square roots.
A.REI.B.4.B
Graph quadratic functions using $${x-}$$intercepts and vertex.
A.APR.B.3F.IF.B.4F.IF.C.7.AF.IF.C.8.A
Topic C: Interpreting Solutions of Quadratic Functions in Context
Interpret quadratic solutions in context.
A.CED.A.1F.IF.B.4F.IF.B.5F.IF.C.8.A
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