Addition and subtraction of functions

Addition and subtraction of linear functions

Addition of functions and the polynomial form

Sum of quadratic functions

The sum of a quadratic and a linear function

Algebraic operations on the two sides of an comparison

Changing an equation by the addition of functions

Changing functions

Rate of change of linear functions

Constant and non-constant rate

Quadratic growth

Allowance

Building blocks

Saving the elephants

Correspondence rules and quadratic growth

Growing shapes

Motion at changing speed

Comparisons between two functions

Comparisons and operations performed on comparisons

Comparisons: algebraic operations on the two sides

Algebraic operations on the sides of the comparison

Constructing inequalities

Changing an equation by of adding functions

Equality between quadratic and linear functions: changing the equation

Properties of the difference graph

Constructing equalities

Pairs of numbers with equal sums and products

Cutting circles

Quadratic comparisons and graph transformations

Constructing inequalities

Constructing inequalities

Inequality between a linear and a quadratic function

Inequality between two quadratic functions

Quadratic inequality: changing the solution

Correspondence rules

Representations of linear functions

Equivalent expressions of functions

Describing a trip

Addition and subtraction of linear functions

Difference functions

The difference equation

Equivalent equations

Solving equations

Quadratic equations of the type [vertex form]=[constant]

Quadratic equations of the type [quadratic function]=[constant]

Difference function: from general quadratic functions to quadratic functions of the type h(x)=0

Algebraic operations on the sides of a comparison

Equivalent expressions

Equivalent expressions of functions

Verbal descriptions of equivalent functions

Same correspondence rules, different stories

Features from value tables

Emphasizing intersections

Equivalent quadratic expressions

Reading information about functions from correspondence rules

Numeric surprises

Graph transformations and the vertex form

Same function, different correspondence rules

Factoring

Families of functions

Transformations of graphs

Families of functions

Parametric family and sub-families

Graph transformations and the vertex form

Family properties - 1

Family properties - 2

Functions defined on intervals

Functions defined on intervals

Dangerous speed

Accelerating and decelerating

Graph transformations

Transformations of graphs

Product form and transformations

Transforming one function into another

Graph transformations and the vertex form

Changing a function using transformations

Increase and decrease of functions

Rate of change of linear functions

Properties of the difference graph

Relations between functions and their sum

Linear functions in various representations

Deriving information about functions from correspondence rules

Multiplying more than two linear functions

Linear functions: various representations

Linear functions in various representations

Different descriptions of a trip

Addition and subtraction of linear functions

Operations between functions

Addition and subtraction of linear functions

Relations between functions and their sum

Phenomena: emphasizing data through correspondence rules

Emphasizing data through correspondence rules

Equivalent expressions of functions

Families of functions

Phenomena: graphs describing motion

Graphs describing motion

Rides

Phenomena: manner of motion

Various ways to describe motion

Runway

Phenomena: motion at constant acceleration

Constant acceleration

Phenomena: schematic description of motion

Journeys at two speeds

Phenomena: speed

Features from value tables

Average velocity

Points of intersections with the axes and other lines

Linear functions in various representations

Reading information about a function from correspondence rules

Polynomials

Polynomials

Multiplying more than two linear functions

Product of linear functions

Products of linear functions

What times what?

Same function, different correspondence rules

Factoring the product of linear functions

Optimal fencing

Products of more than two linear functions

Art museum

Algebraic operations on the sides of a comparison

Relations between various shapes and the correspondence rules of quadratic functions

Product form and transformations

Quadratic functions: construction by transformations of f(x)=x²

Transformations of f(x)=x²

Vertex form

Constructing functions by transformations of f(x)=x²

Quadratic functions: describing phenomena

Constructing quadratic functions using points

Green areas

Space for rabbits: optimization problem

Optimal fencing

Runway

Stopping a car

Speed limits

Holiday cards

Growing shapes

Jackpot

Matchstick shapes

Cutting the cake

Sandwitch sale

Electronic magazine

Quadratic functions: families

Families of functions

Parametric families

A Parametric family and sub-family

Graph transformations and the vertex form

Constructing families of functions with given properties

Family properties - 1

Quadratic functions: optimization phenomena

Deriving information about a function from correspondence rules

Same function, different correspondence rules

Rabbit Cage: an optimization problem

Optimal fencing

Designing a box: an optimization problem

Sandwitch sales

T-shirt prices

Electronic magazine

Art museum

Chocolate imports

Quadratic functions: polynomial form

Relations between various forms and the correspondence rules of quadratic functions

Addition of functions and the polynomial form

Constructing functions in polynomial form

Quadratic functions: product form

Relations between various forms and the correspondence rules of quadratic functions

Product form and transformations

Same function, different correspondence rules

Factoring the product of linear functions

Optimal fencing

Multiplying more than two linear functions

Quadratic functions: properties

Constructing functions

Features from value tables

Vertex paths

Graph transformations and the vertex form

Quadratic functions: special points

Partial pictures

Quadratic functions: various representations

Graph transformations and the vertex form

Matchstick shapes

Pricing shirts

Motion at variable speed

Stopping a train

Stopping a car

Quadratic functions: vertex form

Relations between various forms and the correspondence rules of quadratic functions

Vertex form

Conversion to the vertex form

Scale

Partial pictures

Slope of the function graph

Linear function in various representations

Properties derived from tables

Transformations: graph translation

Transformations of graphs

Graph transformations and the vertex form

Transforming one function into another

Transformations of f(x)=x²

Converting to vertex form

Quadratic comparisons and graph transformations

Product form and transformations

Changing a function by transformation

Transformations: reflection

Transformations of graphs

Graph transformations and the vertex form

Transforming one function into another

Product form and transformations

Changing a function by transformation

Equality between quadratic and linear functions: changing the equation

Transformations: stretching

Graph transformations and the vertex form

Transforming one function into another

Transformations of f(x)=x²

Product form and transformations

Changing a function by transformation

Quadratic comparisons and graph transformations

Equality between quadratic and linear functions: changing the equation

Value tables

Value table and rate of change

Linear function in various representations

Properties derived from tables

Graph transformations and the vertex form

Constant and non-constant rates

Structures from cubes

Growing shapes