ALEX Classroom Resource

  

Finding X- and Y-intercepts of Quadratic Functions | Algebra 1: Module 10 - Topic 4

  Classroom Resource Information  

Title:

 Finding X- and Y-intercepts of Quadratic Functions | Algebra 1: Module 10 - Topic 4

URL:

 https://aptv.pbslearningmedia.org/resource/whro-video-classroom-mod10-topic4/finding-x-and-y-intercepts-of-quadratic-functions-algebra-1-module-10-topic-4/

Content Source:

 PBS
Type: Audio/Video

Overview:

In this program students learn to find x- and y-intercepts of quadratic functions.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
Accelerated
27. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). [Algebra I with Probability, 25]
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a contextual situation shown by a graph, a description of a relationship, or two input-output pairs,
  • Create a linear or exponential function that models the situation.
  • Create arithmetic and geometric sequences from the given situation.
  • Justify the equality of the sequences and the functions mathematically and in terms of the original sequence.
Teacher Vocabulary:
  • Arithmetic sequence
  • Geometric sequence
  • Linear function
  • Exponential function
    • Knowledge:
    Students know:
    • That linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
    • Properties of arithmetic and geometric sequences.
    Skills:
    Students are able to:
    • Accurately recognize relationships within data and use that relationship to create a linear or exponential function to model the data of a contextual situation.
    Understanding:
    Students understand that:
    • Linear and exponential functions may be used to model data that is presented as a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
    • Linear functions have a constant value added per unit interval, and exponential functions have a constant value multiplied per unit interval.
    Diverse Learning Needs:
    Mathematics
    MA2019 (2019)
    Grade: 8
    Accelerated
    32. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

    a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

    b. Graph piecewise-defined functions, including step functions and absolute value functions.

    c. Graph exponential functions, showing intercepts and end behavior. [Algebra I with Probability, 30]
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a symbolic representation of a function (including linear, quadratic, absolute value, piecewise-defined functions, and exponential,
    • Produce an accurate graph (by hand in simple cases and by technology in more complicated cases) and justify that the graph is an alternate representation of the symbolic function.
    • Identify key features of the graph and connect these graphical features to the symbolic function, specifically for special functions:
      A. quadratic or linear (intercepts, maxima, and minima) and piecewise-defined functions, including step functions and absolute value functions (descriptive features such as the values that are in the range of the function and those that are not).
      b. exponential (intercepts and end behavior).
    Teacher Vocabulary:
    • x-intercept
    • y-intercept
    • Maximum
    • Minimum
    • End behavior
    • Linear function
    • Factorization
    • Quadratic function
    • Intercepts
    • Piecewise function
    • Step function
    • Absolute value function
    • Exponential function
    • Domain
    • Range
    • Period
    • Midline
    • Amplitude
    • Zeros
    Knowledge:
    Students know:
    • Techniques for graphing.
    • Key features of graphs of functions.
    Skills:
    Students are able to:
    • Identify the type of function from the symbolic representation.
    • Manipulate expressions to reveal important features for identification in the function.
    • Accurately graph relationships.
    Understanding:
    Students understand that:
    • Key features are different depending on the function.
    • Identifying key features of functions aid in graphing and interpreting the function.
    Diverse Learning Needs:
    Mathematics
    MA2019 (2019)
    Grade: 9-12
    Algebra I with Probability
    25. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a contextual situation shown by a graph, a description of a relationship, or two input-output pairs,
    • Create a linear or exponential function that models the situation.
    • Create arithmetic and geometric sequences from the given situation.
    • Justify the equality of the sequences and the functions mathematically and in terms of the original sequence.
    Teacher Vocabulary:
    • Arithmetic and geometric sequences
    • Arithmetic sequence
    • Geometric sequence
    • Exponential function
    Knowledge:
    Students know:
    • That linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
    • Properties of arithmetic and geometric sequences.
    Skills:
    Students are able to:
    • Accurately recognize relationships within data and use that relationship to create a linear or exponential function to model the data of a contextual situation.
    Understanding:
    Students understand that:
    • Linear and exponential functions may be used to model data that is presented as a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
    • Linear functions have a constant value added per unit interval, and exponential functions have a constant value multiplied per unit interval.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    ALGI.25.1: Define linear function and exponential function.
    ALGI.25.2: Define arithmetic sequence, geometric sequence, and input-output pairs.
    ALGI.25.3: Define sequences and recursively-defined sequences.
    ALGI.25.4: Recognize that sequences are functions whose domain is the set of all positive integers and zero.
    ALGI.25.5: Given a chart, write an equation of a line.
    ALGI.25.6: Given a graph, write an equation of a line.
    ALGI.25.7: Given two ordered pairs, write an equation of a line.

    Prior Knowledge Skills:
    • Given a function, create a rule.
    • Recognize numeric patterns.
    • Recall how to complete input/output tables.
    • Demonstrate how to plot points on a Cartesian plane using ordered pairs.
    • Define function, ordered pairs, input, output.
    • Graph a linear equation given the slope-intercept form of an equation.
    • Graph a function given the slope-intercept form of an equation.
    • Identify the slope-intercept form (y=mx+b) of an equation where m is the slope and y is the y-intercept.
    • Generate the slope of a line using given ordered pairs.
    • Recall the rules for multiplying integers.
    • Define quotient, divisor, and integer.
    • Solve addition and subtraction of multi-digit whole numbers.
    • Solve addition and subtraction of multi-digit decimal numbers (emphasis on alignment).
    • Recall basic multiplication and division facts.
    • Solve multiplication problems involving multi-digit whole numbers and decimal numbers.
    • Solve division problems involving multi-digit whole numbers and decimal numbers.
    Alabama Alternate Achievement Standards
    AAS Standard:
    M.A.AAS.12.24 Given a simple linear function on a graph, select the model that represents an increase by equal amounts over equal intervals.
    Mathematics
    MA2019 (2019)
    Grade: 9-12
    Algebra I with Probability
    30. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

    a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

    b. Graph piecewise-defined functions, including step functions and absolute value functions.

    c. Graph exponential functions, showing intercepts and end behavior.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    Given a symbolic representation of a function (including linear, quadratic, absolute value, piecewise-defined functions, and exponential,
    • Produce an accurate graph (by hand in simple cases and by technology in more complicated cases) and justify that the graph is an alternate representation of the symbolic function.
    • Identify key features of the graph and connect these graphical features to the symbolic function, specifically for special functions:
        quadratic or linear (intercepts, maxima, and minima) and piecewise-defined functions, including step functions and absolute value functions (descriptive features such as the values that are in the range of the function and those that are not).
      1. Exponential (intercepts and end behavior).
    Teacher Vocabulary:
    • x-intercept
    • y-intercept
    • Maximum
    • Minimum
    • End behavior
    • Linear function
    • Factorization
    • Quadratic function
    • Intercepts
    • Piece-wise function
    • Step function
    • Absolute value function
    • Exponential function
    • Domain
    • Range
    • Period
    • Midline
    • Amplitude
    • Zeros
    Knowledge:
    Students know:
    • Techniques for graphing.
    • Key features of graphs of functions.
    Skills:
    Students are able to:
    • Identify the type of function from the symbolic representation.
    • Manipulate expressions to reveal important features for identification in the function.
    • Accurately graph any relationship.
    Understanding:
    Students understand that:
    • Key features are different depending on the function.
    • Identifying key features of functions aid in graphing and interpreting the function.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    ALGI.30.1: Define piecewise-defined functions and step functions.
    ALGI.30.2: Graph functions expressed symbolically by hand in simple cases.
    ALGI.30.3: Graph functions expressed symbolically using technology for a more complicated case.

    a.
    ALGI.30.4: Graph quadratic functions showing maxima and minima.
    ALGI.30.5: Graph quadratic functions showing intercepts.
    ALGI.30.6: Graph linear functions showing intercepts.

    b.
    ALGI.30.7: Define square root, cube root, and absolute value function.
    ALGI.30.8: Graph piecewise-defined functions.
    ALGI.30.9: Graph step functions.
    ALGI.30.10: Graph cube root functions.
    ALGI.30.11: Graph square root functions.
    ALGI.30.12: Graph absolute value functions.

    c.
    ALGI.30.13 Identify exponential numbers as repeated multiplication.
    ALGI.30.14 Rewrite exponential numbers as repeated multiplication.

    Prior Knowledge Skills:
    • Demonstrate how to plot points on a coordinate plane using ordered pairs from a table.
    • Graph a function given the slope-intercept form of an equation.
    • Recognize the absolute value of a rational number is its' distance from 0 on a vertical and horizontal number line.
    • Define absolute value and rational numbers.
    • Recall how to plot ordered pairs on a coordinate plane.
    • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
    Alabama Alternate Achievement Standards
    AAS Standard:
    M.A.AAS.12.30 Given the graph of a linear function, identify the intercepts, the maxima, and minima.

    Tags: factor, functions, quadratic, xintercept, yintercept
    License Type: Public Domain
    For full descriptions of license types and a guide to usage, visit :
    https://creativecommons.org/licenses
    AccessibilityAudio resources: includes a transcript or subtitles
    Comments
      This resource provided by:  
    Author: Kristy Lacks
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