What is the difference between a quadratic equation and a quadratic function? I cannot dicepher the difference between a quadratic equation and a quadratic function. I read the following "A quadratic equation can tell us a lot about the graph of a quadratic function." I see the following equation:
f(x) = 10x^2 - 8x

That to me is a quadratic equation, because the x term is squared. And the x squared is the highest power on x. This quadratic equation can be broken down into a linear equation by factoring.
How is this different from a quadratic function? 
 A: My explanation is that a quadratic equation is a set of terms of the form (in general): $ax^2+bx+c=0$. A quadratic function is one where the right-hand constant (call it $f$) is allowed to vary with $x$, thus giving: $f(x)=ax^2+bc+c$.
A: $$y=f(x)=10x^2-8x$$
is a quadratic function: the set of all points in the plane of the form $\;\left(x\,,\,10x^2-8x\right)\;$
A quadratic equation "asks" for what value(s) of $\;x\;$ it equals some definite values, for example $\;10x^2-8x=0\;,\;\;10x^2-8x=16\;$ are quadratic equations
A: A quadratic equation is made for the purpose of solving for a specific variable and so it will the equation will always be equal to a number.
For example: 0 = 10x(squared) + 4
A quadratic function is made for the purpose of graphing and so it will either be set to be equal to f(x) or y.
For example: f(x) = 10x(squared) + 4x
Another example: y = 10x(squared) + 4x
Also, both a quadratic function and a quadratic equation can have x to the second power.
So lastly, I think the difference between a function and an equation lies in what it has been set equal to, and in the purpose (whether it be to solve, or to graph).
