Is a Quadratic equation a function?

Solution 1:

I think you're getting your dependent and independent variables mixed up. Given a quadratic equation, say $y=ax^2+bx+c$, the independent variable is $x$, whereas the dependent variable is $y$. Quadratics have at most two solutions for every output (dependent variable), but each input (independent variable) only gives one value.

Solution 2:

The function $f(x)=ax^2+bx+c$ is a quadratic function.

Now, if you try to solve a quadratic equation, you get often two solutions, but this is not the same as calculating the function. What does this actually shows is that the quadratic function takes many values twice, and in particular doesn't have an inverse.