Curriculum / Math / 9th Grade / Unit 7: Quadratic Functions and Solutions / Lesson 5
Math
Unit 7
9th Grade
Lesson 5 of 13
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Identify solutions to quadratic equations using the zero product property (equations written in intercept form).
The core standards covered in this lesson
A.APR.B.3 — Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
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.
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
Consider the equation $${a\times b=0}$$. What can you conclude about the values of $$a$$ and $$b$$?
Consider the equation $$(a+2)(b-1)=0$$. What can you conclude about the values of $$a$$ and $$b$$?
The solutions to a quadratic equation are given by the $${x-}$$intercepts of the graph. What are the solutions to the quadratic equation graphed below?
The equation for the parabola shown is $$y=({x-}3)(x+2)$$. Show algebraically that the solutions to the quadratic equation are the same as those seen in the graph.
A quadratic function is shown in the graph below.
The equation for this function is $${y=(x+a)(2x+b)}$$. What are possible values for $$a$$ and $$b$$?
A set of suggested resources or problem types that teachers can turn into a problem set
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For each equation below, use the zero product property to find all solutions. Explain each step in your reasoning.
a. $${x(13-4x)=0}$$
b. $${7(y+12)=0}$$
c. $${(x-19)(x+3)=0}$$
d. $${(y-6)(3z-4)=0}$$
Zero Product Property 3, accessed on July 2, 2018, 10:37 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.
Which equation represents the graph shown below? Explain your reasoning.
a. $${y=(x-3)(x+6)}$$
b. $${y=(x+3)(x-6)}$$
c. $${y=(x-3)(x-6)}$$
d. $${y=(x+3)(x+6)}$$
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 4
Lesson 6
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
A.APR.B.3 F.IF.C.8.A
Factor quadratic equations and identify solutions (when leading coefficient is equal to 1).
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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