Finding Components of Quadratic Functions - Overview Video

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This video will explain how to identify components of quadratic functions and solve the function for each variable. 

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.

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.

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

CR Resource Type

Audio/Video

Resource Provider

CK-12

License Type

Custom
ALSDE LOGO