Quadratic Functions and Solutions

Lesson 6

Math

Unit 7

9th Grade

Lesson 6 of 13

Objective


Factor quadratic equations and identify solutions (when leading coefficient is equal to 1).

Common Core Standards


Core Standards

  • A.SSE.A.1.A — Interpret parts of an expression, such as terms, factors, and coefficients.
  • A.SSE.B.3.A — Factor a quadratic expression to reveal the zeros of the function it defines.

Criteria for Success


  1. Understand factoring as the reverse process of multiplying.
  2. Understand the value of factoring a quadratic equation in revealing the solutions of the equation.
  3. Distinguish between quadratic, linear, and constant terms in a quadratic expression and use them to factor efficiently.
  4. Factor, where possible, quadratic equations with leading coefficients equal to 1.

Tips for Teachers


Lessons 6 and 7 focus on factoring quadratic trinomials into a product of two linear binomials. In Lesson 6, all equations have a leading coefficient of 1, and in Lesson 7, students work with examples where the leading coefficient is not equal to 1. Depending on the needs of your students, these lessons may be left as separate lessons or combined into one lesson. There are additional opportunities for factoring practice and mastery in Lessons 8–10. 

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Anchor Problems

25-30 minutes


Problem 1

The table below shows pairs of equivalent expressions. 

a.  $${(x+3)(x+2)}$$

$${{x^2}+5x+6}$$

b.  $${(x+1)(x+8)}$$

$${{x^2}+9x+8}$$

c.  $${(x-7)(x-3)}$$

$${{x^2}-10x+21}$$

d.  $${(x+10)(x-4)}$$

$${{x^2}+6x-40}$$

e.  $${(x-10)(x+4)}$$

$${{x^2}-6x-40}$$

f.  $${(x+5)(x-4)}$$

$${x^2}$$_____$$x$$_____

g.  $$(x$$____$$)(x$$____$$)$$

$${x^2}-11x+24$$

a.  What relationship do you notice between the values in the expressions in the left column and the values in the expressions in the right column?

b.  Complete the missing information in rows (f) and (g).

Guiding Questions

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Problem 2

Find the roots of the function represented by the equation $${y=x^2-9x-36}$$.

Guiding Questions

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Problem 3

Solve the quadratic equation. Check your solutions algebraically. 

$${x^2+x-6=6}$$

Guiding Questions

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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.

Target Task

5-10 minutes


Where possible, write each quadratic trinomial as a product of two linear binomials.

a.  $${x^2-12x+11}$$

b.  $${x^2+2x-48}$$

c.  $${x^2+6x-40}$$

d.  $${x^2-14x-40}$$

e.  $${x^2+22x+40}$$

f.  $${x^2-18x-40}$$

g.  $${x^2+3x-40}$$

h.  $${x^2+13x+40}$$

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.

Next

Factor quadratic equations and identify solutions (when leading coefficient does not equal 1).

Lesson 7
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Quadratic Functions

Topic B: Factoring and Solutions of Quadratic Equations

Topic C: Interpreting Solutions of Quadratic Functions in Context

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