Learning Resource Type

Classroom Resource

Recognizing Quadratic Functions

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

Travis found the following equation in his math book

d=rt16t2

It is an equation to calculate velocity. In fact, it is a function. Being an avid sports player, Travis was very interested in figuring out how to use the equation, but he isn’t even sure what kind of a function it is. Can you identify this function? In this concept, you will learn to recognize a quadratic function as an equation in two variables with a specific form.

This informational material will help students identify key features of and solutions for quadratic functions.  Practice questions with a PDF answer key are provided.  

    Mathematics (2019) Grade(s): 09-12 - Precalculus

    MA19.PRE.20

    Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a clear-cut solution. Construct a viable argument to justify a solution method. Include equations that may involve linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric functions, and their inverses.

    Unpacked Content

    UP:MA19.PRE.20

    Vocabulary

    • equivalence
    • viable

    Knowledge

    Students know:
    • How to solve equations using a reasoning process centered around inverse operations and order of operations

    Skills

    Students are able to:
    • Solve linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric equations (including their inverses) using multiple solution strategies and explain each step in the solution path.
    • Construct a viable argument to justify a chosen solution path used to solve a linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric equation (including their inverses).
    • Compare the steps in each and determine which solution path is most efficient, given an equation with multiple solution paths.
    • Explain when an equation has no solution or infinitely many solutions.

    Understanding

    Students understand that:
    • The process of solving equations is a reasoning process to determine a solution that satisfies the equation rather than a procedural list of steps.
    • An equation has no solution because there is no value that can maintain equivalency and an equation has infinitely many solutions because all values used for the variable create a true equivalency statement
    Mathematics (2019) Grade(s): 09-12 - Precalculus

    MA19.PRE.24

    Compare and contrast families of functions and their representations algebraically, graphically, numerically, and verbally in terms of their key features. Note: Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries (including even and odd); end behavior; asymptotes; and periodicity. Families of functions include but are not limited to linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, trigonometric, and their inverses.

    Unpacked Content

    UP:MA19.PRE.24

    Vocabulary

    • Function
    • Relative Maximum
    • Relative Minimum
    • Symmetry (Even/Odd)
    • End Behavior
    • Asymptotes
    • Intercepts
    • Increasing/Decreasing Intervals
    • Periodicity
    • Absolute Maximum
    • Absolute Minimum

    Knowledge

    Students know:
    • Properties of functions and make connections between different representations of the same function

    Skills

    Students are able to:
    • Compare properties of functions when represented in different ways (algebraically, graphically, numerically in tables or by verbal descriptions).

    Understanding

    Students understand that:
    • Each representation provides a unique perspective of the function.
    • Different representations are most appropriate for revealing certain key features of the function
    Link to Resource

    Resource Provider

    Other

    Resource Provider other

    CK-12
    Accessibility
    License

    License Type

    CUSTOM
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