The degree of the constant term in a quadratic (or any polynomial) is $0$. Say, I have the following quadratic function: $$f(x) = 2x^2 + 4x +7$$
Since the degree of the constant term is $0$, I can also write the quadratic function like such: $$f(x) = 2x^2 + 4x^1 + 7x^0$$
If I plug in $x = 0$ into the function, I'm supposed to get the constant term. $$f(0) = 2(0)^2 + 4(0)^1 + 7(0)^0$$
But $0^0$ isn't defined. So does that mean that the $f(0)$ isn't defined? But if I didn't treat the constant as being multiplied by $x^0$, then I'll have an answer which equals $7$: $$f(0) = 2(0)^2 + 4(0)^1 + 7$$ $$f(0) = 7$$
I'm still learning about quadratics so I'd really appreciate someone clear me up about this without going into some advanced stuff.
We usually avoid using notation that will result in us having to deal with $0^0$ terms for exactly the reason you're describing, and hence we usually write polynomials as $p(x) = a_n x^n + \ldots + a_1 x + a_0$. However, we may also write the polynomial as $p(x) = \sum_{i = 0}^n a_i x^i$, which clearly does include an $x^0$ term. So what gives?
Broadly speaking, when it is clear that the assumption of $x^0 = 1$ even when $x = 0$ won't break anything, then it's ok to use that kind of shorthand. If needed, we can justify that we "won't break anything" by noting that this notation is 100% correct for $x \neq 0$, and also that it all still behaves nicely in the limit as $x$ approaches 0, i.e. $\lim_{x \rightarrow 1} x^0 = 1$ and hence defining $x^0 := 1$ even when $x = 0$ for this purpose results in continuity for all the polynomials, which is definitely a nice thing to have.
Of course, you can't use $0^0 = 1$ all the time - if we're looking at limits of the exponent, then $\lim_{y \rightarrow 0} 0^y = 0$ and so $\lim_{(x, y) \rightarrow (0, 0)} x^y$ is undefined. Thankfully, polynomials are only defined as having exponents that are non-negative integers, so that usually isn't something we have to worry about. If it is, then you might need to look at whether the $(0, 0)$ limit is going to be an issue and define your notation carefully to avoid it.