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# Multiples of Quadratic Equations and their Graphs

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Two quadratic equations that are multiples of each other are actually the same equation, and that they don't count as being "more than one QE that have the same solution set". However, if you plot the two equations on a graph, will they be different from each other, but have the same x-axis intercepts, which are the answer set?
If they are different graphs, does that mean that they are really two different equations?

Please explain, and provide an example.

#### Solution Preview

Hello and thank you for posting your question to Brainmass.

One has to differentiate between function and equation.

Think of a function as a number-blender. You put in a number, press the button and out comes another number.
That what a function does it matches between two sets of numbers.

For example f(n) = n! matches between an integer and its factorial. I throw in 2 and I get back 4. I throw in 5 and I get back 120.

The input set is the "domain" while the output set is called the "range".

So one can say that the question a function represents is:

"If I input this number, what output will I get?"

An equation is a totally different construct.
An equation is a logical entity. It is a statement. And statements can be either "True" or "False".

For example the equation 2 = 4 is a false statement, while ...

#### Solution Summary

Multiples of quadratic equations and their graphs are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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