Curriculum / Math / 9th Grade / Unit 7: Quadratic Functions and Solutions / Lesson 6
Math
Unit 7
9th Grade
Lesson 6 of 13
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Factor quadratic equations and identify solutions (when leading coefficient is equal to 1).
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.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 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.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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).
Find the roots of the function represented by the equation $${y=x^2-9x-36}$$.
Solve the quadratic equation. Check your solutions algebraically.
$${x^2+x-6=6}$$
A set of suggested resources or problem types that teachers can turn into a problem set
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
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.  $${x^2+13x+40}$$
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.
Lesson 5
Lesson 7
Topic A: Features of Quadratic Functions
Compare quadratic, exponential, and linear functions represented as graphs, tables, and equations.
F.IF.B.4 F.LE.A.2
Identify key features of a quadratic function represented graphically. Graph a quadratic function from a table of values.
F.IF.B.4 F.IF.C.7.A
Calculate and compare the average rate of change for linear, exponential, and quadratic functions.
F.IF.B.4 F.IF.B.6 F.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.1 A.SSE.A.2 A.SSE.B.3.A
Identify solutions to quadratic equations using the zero product property (equations written in intercept form).
A.APR.B.3 F.IF.C.8.A
A.SSE.A.1.A A.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.A A.SSE.A.2 A.SSE.B.3.A
Factor special cases of quadratic equations—perfect square trinomials.
A.SSE.A.2 A.SSE.B.3.A
Solve quadratic equations by factoring. Compare solutions in different representations (graph, equation, and table).
A.SSE.B.3.A F.IF.C.8.A F.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.3 F.IF.B.4 F.IF.C.7.A F.IF.C.8.A
Topic C: Interpreting Solutions of Quadratic Functions in Context
Interpret quadratic solutions in context.
A.CED.A.1 F.IF.B.4 F.IF.B.5 F.IF.C.8.A
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