Learning Resource Type

Classroom Resource

Solving Quadratic Equations With the Zero Product Property: Algebra 1, Episode 13: Unit 7, Lesson 4 | Illustrative Math

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

In this video lesson, students learn about the zero product property. They use it to reason about the solutions to quadratic equations that each have a quadratic expression in the factored form on one side and 0 on the other side. They see that when an expression is a product of two or more factors and that product is 0, one of the factors must be 0. Students make use of the structure of a quadratic expression in factored form and the zero product property to understand the connections between the numbers in the form and the x-intercepts of its graph (MP7).

    Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

    MA19.8A.6

    Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

    Unpacked Content

    UP:MA19.8A.6

    Vocabulary

    • Function
    • zero of a function
    • Roots
    • parabola
    • vertex form of a quadratic expression
    • Minimum and maximum value
    • Axis of symmetry
    • Completing the square
    • Exponential growth and decay

    Knowledge

    Students know:
    • The vertex form of a quadratic expression asf (x) = a(x
    • h)2 + k, where (h, k) is the vertex of the parabola.
    • Techniques for generating equivalent forms of an algebraic expression including factoring and completing the square for quadratic expressions and using properties of exponents,
    • When one form of an algebraic expression is more useful than an equivalent form of that same expression to solve a given problem.

    Skills

    Students are able to:
    • Use algebraic properties including properties of exponents to produce equivalent forms of the same expression by recognizing underlying mathematical structures,
    • Factor quadratic expressions with leading coefficient of one
    • Complete the square in quadratic expressions.

    Understanding

    Students understand that:
    • An expression may be written in various equivalent forms.
    • Some forms of the expression are more beneficial for revealing key properties of the function.
    Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

    MA19.A1.6

    Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

    Unpacked Content

    UP:MA19.A1.6

    Vocabulary

    • Quadratic expression
    • Zeros
    • Complete the square
    • Roots
    • Zeros
    • Solutions
    • x-intercepts
    • Maximum value
    • Minimum value
    • Factor
    • Roots
    • Exponents
    • Equivalent form
    • Vertex form of a quadratic expression

    Knowledge

    Students know:
    • Techniques for generating equivalent forms of an algebraic expression, including factoring and completing the square for quadratic expressions and using properties of exponents.
    • When one form of an algebraic expression is more useful than an equivalent form of that same expression to solve a given problem.

    Skills

    Students are able to:
    • Use algebraic properties including properties of exponents to produce equivalent forms of the same expression by recognizing underlying mathematical structures.
    • Factor quadratic expressions.
    • Complete the square in quadratic expressions.
    • Use the vertex form of a quadratic expression to identify the maximum or minimum and the axis of symmetry.

    Understanding

    Students understand that:
    • Making connections among equivalent expressions reveals the roles of important mathematical features of a problem.
    Link to Resource

    CR Resource Type

    Audio/Video

    Resource Provider

    PBS
    Accessibility

    Accessibility

    Video resources: includes closed captioning or subtitles
    License

    License Type

    Custom
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