<s>[INST] Here is the question:

Let $f(x)$ be a polynomial of degree 2 such that $f(2)=9$, $f(-5)=-84$, and $f(-2)=7$. Then the value of $f(5)$ is:

I am looking for a model solution that can be used to create a model in excel or libreoffice since the problem requires some rather complicated equations.

Before we start, I am aware that the original function can be expressed as:

f(x) = ax^2 + bx + c

This is a quadratic polynomial with degree two, and we are looking for the values of a, b, and c.

Now, we can make three equations using the givens:
9 = a(2)^2 + b(2) + c = 4a + 2b + c
-84 = a(-5)^2 + b(-5) + c = 25a - 5b + c
7 = a(-2)^2 + b(-2) + c = 4a - 2b + c

This is the starting point of the solution. Can you help me come up with the rest of the solution and build the model?[/INST]