How Many Solutions?: Algebra 1, Episode 14: Unit 7, Lesson 5 | Illustrative Math

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

7, 8, 9, 10, 11, 12

Overview

This video lesson builds on the idea that both graphing and rewriting quadratic equations in the form of expression = 0 are useful strategies for solving equations. It also reinforces the ties between the zeros of a function and the horizontal intercepts of its graph, which students began exploring in an earlier unit.

Here, students learn that they can solve equations by rearranging them into the form expression = 0, graphing the equation y = expression, and finding the horizontal intercepts. They also notice that dividing each side of a quadratic equation by a variable is not reliable because it eliminates one of the solutions. As students explain why certain maneuvers for solving quadratic equations are acceptable and others are not, students practice constructing logical arguments.

 

Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.24

Explain why the x-coordinates of the points where the graphs of the equations $y = f(x)$ and $y = g(x)$ intersect are the solutions of the equation $f(x) = g(x)$. Limit to linear equations. [Algebra I with Probability, 19]

UP:MA19.7A.24

Vocabulary

  • x-intercepts
  • y-intercepts
  • Point of intersection
  • One solution

Knowledge

Students know:
  • That a point of intersection between two linear functions represents one solution to those functions.

Skills

Students are able to:
  • Use mathematical language to explain why the x-coordinates are the same at intersection for y = f(x) and y = g(x).

Understanding

Students understand that:
  • That in cases of a system of linear equations, there is sometimes only one, common point for each one that yields a solution. This is different from previous experiences with single linear equations where every point on its line is a solution set.
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.20

Explain why the x-coordinates of the points where the graphs of the equations $y = f(x)$ and $y = g(x)$ intersect are the solutions of the equation $f(x) = g(x)$.

UP:MA19.8A.20

Vocabulary

  • Functions
  • Successive approximations
  • Linear functions
  • Quadratic functions
  • Absolute value functions
  • Exponential functions
  • Intersection point(s)

Knowledge

Students know:
  • Defining characteristics of linear, quadratic, absolute value, and exponential graphs.
  • Methods to use technology, tables, and successive approximations to produce graphs and tables.

Skills

Students are able to:
  • Determine a solution or solutions of a system of two functions.
  • Accurately use technology to produce graphs and tables for linear, quadratic, absolute value, and exponential functions.
  • Accurately use technology to approximate solutions on graphs.

Understanding

Students understand that:
  • When two functions are equal, the x coordinate(s) of the intersection of those functions is the value that produces the same output (y-value) for both functions.
  • Technology is useful to quickly and accurately determine solutions and produce graphs of functions.
Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.19

Explain why the x-coordinates of the points where the graphs of the equations $y = f(x)$ and $y = g(x)$ intersect are the solutions of the equation $f(x) = g(x)$.

UP:MA19.A1.19

Vocabulary

  • Functions
  • Linear functions
  • Absolute value functions
  • Exponential functions
  • Intersection

Knowledge

Students know:
  • Defining characteristics of linear, polynomial, absolute value, and exponential graphs.
  • Methods to use technology and tables to produce graphs and tables for two functions.

Skills

Students are able to:
  • Determine a solution or solutions of a system of two functions.
  • Accurately use technology to produce graphs and tables for linear, quadratic, absolute value, and exponential functions.
  • Accurately use technology to approximate solutions on graphs.

Understanding

Students understand that:
  • By graphing y=f(x) and y=g(x) on the same coordinate plane, the x-coordinate of the intersections of the two equations is the solution to the equation f(x) = g(x)

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

Custom
https://aptv.pbslearningmedia.org/resource/im20-math-ep14-75/how-many-solutions/

Custom License Type (URL)

https://aptv.pbslearningmedia.org/help/terms-of-use/#.YD-bCNhKiUk

Accessibility

Video resources: includes closed captioning or subtitles

Approved Date

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