Curriculum / Math / 9th Grade / Unit 8: Quadratic Equations and Applications / Lesson 2
Math
Unit 8
9th Grade
Lesson 2 of 15
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Lesson Notes
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Complete the square.
The core standards covered in this lesson
A.SSE.B.3.B — Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
The foundational standards covered in this lesson
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
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Complete the table with the missing values in order to "complete the square."
Completing the Square by Kate Nowak is made available on Function of Time under the CC BY-NC-SA 3.0 license. Accessed July 12, 2018, 4:32 p.m..
Complete the square in each expression below to include a perfect square binomial.
a. $${x^2+6x+11}$$
b. $${x^2+5x-10}$$
Rewrite each equation into vertex form by completing the square.
a. $${x^2-12x+5=y}$$
b. $${2x^2+16x+3=y}$$
Algebra I > Module 4 > Topic B > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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
Rewriting a Quadratic Expression, accessed on July 12, 2018, 11:55 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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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Complete the square to identify the vertex and solve for the roots of a quadratic function.
Topic A: Deriving the Quadratic Formula
Describe features of the vertex form of a quadratic function and write quadratic equations in vertex form from graphs.
Standards
A.SSE.B.3F.IF.B.4F.IF.C.8
A.SSE.B.3.B
A.REI.B.4.BA.SSE.B.3.B
Solve and interpret quadratic applications using the vertex form of the equation.
A.SSE.B.3.BF.IF.C.8.A
Convert and compare quadratic functions in standard form, vertex form, and intercept form.
F.IF.B.4F.IF.C.9
Derive the quadratic formula. Use the quadratic formula to find the roots of a quadratic function.
A.REI.B.4.A
Determine the number of real roots of a quadratic function using the discriminant of the quadratic formula.
A.REI.B.4.BF.IF.C.7.A
Graph quadratic functions from all three forms of a quadratic equation.
F.IF.C.7.A
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Topic B: Transformations and Applications
Describe transformations to quadratic functions. Write equations for transformed quadratic functions.
F.BF.B.3
Graph and describe transformations to quadratic functions in mathematical and real-world situations.
Write and analyze quadratic functions for projectile motion and falling bodies applications.
A.CED.A.2F.IF.C.8.AF.IF.C.9
Write and analyze quadratic functions for geometric area applications.
A.CED.A.2F.IF.C.8.A
Write and analyze quadratic functions for revenue applications.
A.CED.A.2F.BF.A.1.BF.IF.C.8.A
Solve and identify solutions to systems of quadratic and linear equations when two solutions are present.
A.REI.C.7A.REI.D.11
Solve and identify solutions to systems of quadratic and linear equations when two, one, or no solutions are present.
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