Curriculum / Math / 9th Grade / Unit 7: Quadratic Functions and Solutions / Lesson 10
Math
Unit 7
9th Grade
Lesson 10 of 13
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Lesson Notes
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Solve quadratic equations by factoring. Compare solutions in different representations (graph, equation, and table).
The core standards covered in this lesson
F.IF.C.8.A — Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
F.IF.C.9 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
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
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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
Set A and Set B each include a quadratic function represented as an equation, a graph, and a table.
Determine if all three representations in each set match. If not, explain how you would change one or more of the representations to make them match.
Which quadratic function below has the greatest positive value of $$x$$ as a solution?
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
Match each equation to its graph and table representation.
Card Sort: Parabolas by is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed Aug. 18, 2017, 12:22 p.m..
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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Solve quadratic equations by taking square roots.
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).
Factor special cases of quadratic equations—difference of two squares.
A.SSE.A.1.AA.SSE.A.2A.SSE.B.3.A
Factor special cases of quadratic equations—perfect square trinomials.
A.SSE.A.2A.SSE.B.3.A
A.SSE.B.3.AF.IF.C.8.AF.IF.C.9
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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