Using basic algebra, as shown below, we can prove that the product of two linear functions gives a quadratic function. This property is explored interactively using an applet.
Two links related to the study of the properties of quadratic functions are shown below.
Let h and g be two linear functions of the form
where a and A are non zero constants. It can easily be shown that the product of functions h and g is a quadratic function. Let f be the function obtained as the product of g and h as follows:
f(x) = (h · g) (x) = h(x) · g(x) = ( a x + b ) · ( A x + B )
= a A x 2 + (a B + b A) x + b B
An applet below may be used to explore the properties of the quadratic function f obtained above by changing the parameters a, b , A and B included in the definition of the two linear functions. There are other tutorials you may want to work through later: tutorials on quadratic functions and graphing quadratic functions.
A - Quadratic Functions From Linear Functions : Interactive Tutorial
The button below starts the applet on a separate large screen.
Derivatives of Quadratic Functions: Explore the quadratic function f(x) = ax 2 + b x + c and its derivative graphically and analytically.
Find Vertex and Intercepts of Quadratic Functions - Calculator: An applet to solve calculate the vertex and x and y intercepts of the graph of a quadratic function.
Tutorial on Quadratic Functions (1).
Quadratic Functions - Problems (1).
graphing quadratic functions .
quadratic functions in vertex form .