ALEX Classroom Resource

  

Solving Quadratic Equations with the Zero Product Property

  Classroom Resource Information  

Title:

 Solving Quadratic Equations with the Zero Product Property

URL:

 https://aptv.pbslearningmedia.org/resource/im20-math-ep13-74/solving-quadratic-equations-with-the-zero-product-property/

Content Source:

 PBS
Type: Audio/Video

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 a 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).

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
Accelerated
6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

c. Use the properties of exponents to transform expressions for exponential functions. [Algebra I with Probability, 6]

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, or y = (1.2)t/10, and classify them as representing exponential growth or decay.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Make sense of algebraic expressions by identifying structures within the expression which allow them to rewrite it in useful ways that assist in the solution of given problems
  • Factor a quadratic expression with leading coefficient of one to reveal the zeros of the function it defines
  • Complete the square in a quadratic expression to reveal the maximum or minimum value, the axis of symmetry, and the vertex form of the quadratic expression.
  • Justify their selection of a form for an expression by explaining which features of the expression are revealed by the particular form and how these features aid in resolving a problem situation.
  • Apply exponential properties to expressions and explain and justify the meaning in a contextual situation.
Teacher 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 as f (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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

c. Use the properties of exponents to transform expressions for exponential functions.

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Make sense of algebraic expressions by identifying structures within the expression which allow them to rewrite it in useful ways to assist in the solution of given problems.
  • Produce the useful equivalent forms of expressions,
  • Factor a quadratic expression with leading coefficient of one to reveal the zeros of the function it defines and complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines.
  • Justify their selection of a form for an expression by explaining which features of the expression are revealed by the particular form and how these features aid in resolving a problem situation.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.6.1: Convert an expression to an alternative format.
ALGI.6.2: Recognize the best format for a specific application.
ALGI.6.3: Match equivalent expressions written in different forms.

a.
ALGI.6.4: Define factor, quadratic expression and zero product property.
ALGI.6.5: Factor a quadratic expression.
ALGI.6.6: Use the zero product property to reveal the zeros in the function.
ALGI.6.7: Solve a one-step equation.
ALGI.6.8: Solve a two-step equation.
ALGI.6.9: Determine the Greatest Common Factor (GCF).

b.
ALGI.6.10: Define maximum and minimum value.
ALGI.6.11: Explain the steps for completing the square.
ALGI.6.12: Given a quadratic expression in which the square has already been completed, determine the maximum or minimum values.

c.
ALGI.6.13: Define roots.
ALGI.6.14: Find the equation using the distributive property.
ALGI.6.15: Locate and identify the roots on a graph using the x-intercepts.
ALGI.6.16: Take given roots and convert into a one-step equation set equal to zero.

Prior Knowledge Skills:
  • Identify how many solutions the linear equation may or may not have.
  • Recall how to solve problems using the distributive property
  • Explain the distributive property.
  • Recall solving one-step equations.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.5 Solve simple algebraic equations using real-world scenarios with one variable using multiplication or division.

Tags: expression, factor, solving quadratics, zero product property, zeros
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

This resource has student tasks and practice worksheets that can be used with the video.

  This resource provided by:  
Author: Kristy Lacks
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