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Function Transformations and Mapping Notation Study Guide

This guide provides a comprehensive overview of function transformations, including mapping notation, the effect of parameters on quadratic functions (a, p, q), and how to combine these transformations. It includes examples and explanations for vertical stretches, compressions, reflections, and translations, helping you understand how to alter and graph parent functions like y = x^2.

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Investigating Quadratic Functions in Vertex Form

Investigating Quadratic Functions in Vertex Form

Study notes defining quadratic functions, parabolas, and their characteristics including vertex, axis of symmetry, domain, and range.

  • Quadratic Function
  • Parabola
  • Vertex
  • Minimum Value
  • Maximum Value
  • Direction of Opening
  • Domain
  • Range

Transformations of Quadratic Functions in Vertex Form

Investigating quadratic functions in vertex form through vertical and horizontal translations of the base graph y = x^2.

  • Vertex form of the equation of a quadratic function
  • Vertex
  • Vertical translation
  • Horizontal translation
  • Parameter q
  • Parameter p
  • Mapping notation
  • Base graph

Vertex Form of Quadratic Functions

Vertex Form of Quadratic Functions

Determining characteristics and equations of quadratic functions using the vertex form $y = a(x - p)^2 + q$.

  • Vertex form of the equation of a quadratic function
  • Vertex
  • Direction of opening
  • Parabola
  • Cartesian coordinate plane
  • Graphing quadratic functions

Function Transformations and Mapping Notation

Function Transformations and Mapping Notation

Mathematical notes regarding function transformations, mapping notation, and the effect of parameter a in y = ax^2.

  • Mapping Notation
  • Effect of Parameter a
  • Orientation and shape of the parabola
  • Vertical stretch
  • Vertical compression
  • Reflection in the x-axis
  • Horizontal translation
  • Vertical translation
  • Combining Transformations

Modeling Quadratic Functions with Word Problems

Modeling Quadratic Functions with Frog Jump

A quadratic function models the height of a frog above the surface of water as a function of time.

  • quadratic function
  • y-intercept
  • vertex
  • x-intercept
  • maximum height
  • domain
  • range
  • parabola

Determining the Number of x-intercepts

Determining Number of Quadratic X-Intercepts

  • quadratic function
  • x-intercepts
  • vertex
  • direction of opening
  • parabola

Modeling and Maximizing Revenue with Quadratic Functions

Modeling Revenue with Quadratic Functions

A mathematical modeling example uses a quadratic function to determine maximum revenue and selling price by completing the square.

  • quadratic function
  • revenue
  • mathematical modeling
  • completing the square
  • vertex
  • maximum revenue

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