What is the difference between a quadratic equation and a quadratic function?

Question

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?

Answer 1

$$y=f(x)=10x^2-8x$$

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

Answer 2

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: $f(x)=ax^2+bc+c$.

Answer 3

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).