Overview of Quadratic Functions

 

A Quadratic Function is an Algebraic equation of two variables. One variable

is a second degree while the other is first. One variable is called independent

variable while the other is called the dependent variable.  The independent is

the Horizontal variable while the dependent variable is the Vertical variable.

The sketches below represent all possible solutions to these Quadratic Functions.

 

Quadratic Functions (equations) normally appear in distinct arrangements:

            Standard Form:  f(x) = ax2 + bx + c,                A,B,C are real numbers.

 

Other essential characteristics is that a is nonzero real number and f(x) = y

            also, x is considered the Domain (H values) while y the Range (V values).

 

Each illustration below could exist in an opposite direction.  Up   or  Down

If the domain of X is the real numbers then the Quadratic will cross the X axis twice.

 

y = +x2 –3x                                                                             y = –x2 +9

 

 

 

 

 

 

 


                                                                                                y = x2

 

 

 

 

 

 

 


                                               y = –x2 –x +6                                                                           y= +x2 –x –2

 

 

 

 

 

 

 

 

 

 

 

 


There are many relations between terms of a Quadratic Equation and Solution Set (Curve).

 

Tom Love                       Malone College                    Fall 2007