Quadratic Functions - created from Mind Map

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Definition

Differences

Identifying quadratic functions

Graphing Quadratic Functions

Domain and range

A Quadratic function is any function that can be written in the form y=a^2+bx+c

where a ,b ,and c are real numbers and a≠0.

First Differences

Second Differences

Example

The differences between y-values for a constant change in x-values are called the first differences.

When the first differences have a constant rate of change that is the second different

All quadratic functions have a constant second difference

y=x^2

The First difference is increasing by two so therefore the second difference is 2

Ordered pairs or table

With equations

In a Graph

If you can find the Second Difference and it is constant then it is a quadratic function

If it is righten out or can be written out as y=a^2+bx+c

In a Graph it is represented as a parabola

When graphing quadratic functions you need to make a table with at least 3 points, usually 5 points are best

parabola

Then you graph the points connecting them with a smooth curve

When graphed the shape is a parabola

If a>0 then the parabola is open upwards

If a<0 then the parabola is open downwards

Vertex

The highest or lowest point on a parabola is called the vertex

If the parabola opens upwards the ordered pair at the vertex is its minimum

If the parabola opens downwards the ordered pair at the vertex is its maximum

Domain

Range

The Domain Is all real numbers

If the parabola if facing upwards the eveyrthing above the minimum is the range

If the parabola is facing downwards then everything below the maximum is the range