Lesson 6 | Quadratics | 11th Grade Mathematics

Objective

Complete the square to convert an equation written in standard form to an equation written in vertex form.

Common Core Standards

Core Standards

The core standards covered in this lesson

A.REI.B.4.B — Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Reasoning with Equations and Inequalities

A.REI.B.4.B — Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

A.SSE.B.3.B — Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Seeing Structure in Expressions

A.SSE.B.3.B — Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Write perfect square trinomials from quadratic equations in standard form with a leading coefficient of 1, a negative leading coefficient, and a leading coefficient other than 1.
Describe multiple methods to identifying the vertex from an equation written in standard form.
Show the equivalence of using the axis of symmetry $${-b\over2a}$$ to find the vertex/vertex form and completing the square to find the vertex form.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson is focused on fluency with completing the square. If the pre-assessment indicates that the students do not need an exclusive lesson on this topic, feel free to cut, and incorporate the criteria for success in other future lessons.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Write the following quadratic function in intercept form.

$${f(x)=4x^2+8x+4}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Write the following quadratic function in vertex form by completing the square.

$${g(x)=4x^2+8x-15}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Write the following quadratic functions in vertex form by completing the square.

$${f(x)=-2x^2-8x-6}$$

$${g(x)=3x^2-6x+5}$$

Additional Practice

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.

Include lots of fluency problems and review of other topics from the unit.

Open Middle Create a Quadratic Equation, Given Constraints
Mathematics Vision Project: Secondary Mathematics Two Module 3: Quadratic Equations — Lesson 3.7
Open Middle Maximum Value of a Quadratic in Standard Form

Lesson 5

Lesson 7

Lesson Map

Topic A: Features of Quadratic Functions

Identify features of quadratic functions from equations and use these features to graph quadratic functions. Derive the equation of a parabola.

F.IF.C.7.A F.IF.C.8.A G.GPE.A.2

Identify the y-intercept and vertex of a quadratic function written in standard form through inspection and finding the axis of symmetry. Graph quadratic equations on the graphing calculator.

F.IF.C.7.A F.IF.C.8.A

Write a quadratic equation in intercept form by factoring. Describe the features of a quadratic function written in intercept form.

A.SSE.A.2 A.SSE.B.3.A F.IF.C.8.A

Transform a quadratic function in vertex form. Describe the domain, range, and intervals where the function is increasing and decreasing.

F.BF.B.3 F.IF.B.4 F.IF.C.9

Solve quadratic equations written in vertex form and describe graphical features from vertex form.

A.REI.A.1 A.REI.B.4.B

Complete the square to convert an equation written in standard form to an equation written in vertex form.

A.REI.B.4.B A.SSE.B.3.B

Topic B: Imaginary Solutions and Operating with Complex Numbers

Identify solutions that are non-real from a graph and an equation using the discriminant. Define imaginary and complex numbers.

A.REI.B.4.B N.CN.A.1 N.CN.C.7

Add, subtract, and multiply complex numbers.

N.CN.A.1 N.CN.A.2

Topic C: Applications, Systems, and Inverse with Quadratics

Compare, analyze, and solve quadratic functions in projectile motion application problems.

F.BF.A.1 F.BF.B.3 F.IF.B.6 F.IF.C.8.A F.IF.C.9

Describe features of quadratic functions in the context of a word problem. Evaluate and use function notation to describe contextual situations.

F.BF.A.1 F.IF.B.6 F.IF.C.8.A F.IF.C.9

Identify solutions to a system of a quadratic function and a linear function graphically and algebraically.

A.REI.A.1 A.REI.C.7 A.REI.D.11

Quadratics

Objective

Common Core Standards

Core Standards

Reasoning with Equations and Inequalities

Seeing Structure in Expressions

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Target Task

Additional Practice

Lesson Map

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy