3.6: Quadratic FUNctions

QUADRATIC FUNCTIONS are those funky-looking curved graphs with equations that have multiple xs and confusing exponents in them.

A function f is a QUADRATIC FUNCTION if and only if it fits in the form where a, b, and c are real numbers with a not equal to zero.

What can you figure out from a QUADRATIC FUNCTION?

a: if positive, the funtion opens up; negative, the funtion opens down

it controls the width of the graph

b: controls how the vertex moves along the inversion of the function

c: the y intercept

VERTEX: The minimum or maximum value of the function (minimum if a>0; maximum if a<0)

The coordinate of the vertex of a parabola is

AXIS OF SYMMETRY: That dotted line down the middle of the parabola that runs through the VERTEX.

on the right is the STANDARD FUNCTION

of a parabola with Vertex V(h,k)

You can make your ugly QUADRATIC EQUATION into a fashionable STANDARD EQUATION by simply completing the square, as demonstrated on the right.

Functions

A function is relation that assigns exactly one value in the Range to each value in the Domain.

This does not mean you cannot have multiple values in the Domain assigned to one value in the Range.

The values in the domain are called elements, while the values in the range are called correspondents.



The Domain (or elements of the domain) can also be called:

• X
• Input
• Independent Variable

The Range (or correspondents of the range) can also be called:

• Y
• Output
• Dependent Variable

Y= f(x)

Note: Anytime you see "y-squared" it is not a function because it will have 2 x values for every y value. Also, a circle cannot be a function because it includes "y-squared".

Graphing functions can result in many different types of graphs such as:

Linear Function:

Hyperbola:
Parabola:

Trinomial:

and many others!

So... that's functions... I don't know what else to say so... yeah... I'm gonna stop typing now... and you're just gonna have to deal with it... yeah... well... YOU LOST THE GAME!