# Optimization of Polynomial Function

This is a homework problem, so hints rather than answers would be appreciated.

Problem: Suppose we have the following real observations for $G(x)$: $G(0) = 60$, $G(1) = 100$, and $G(2) = 180$, and we intend to use a polynomial function $ax^2 + bx + c$ to approximate the real observations.

1. Write down the minimization problem.

2. The first order condition will lead to three linear equations involving $a$, $b$, and $c$. Find these three equations, and solve the equations for $a$, $b$, and $c$.

3. Find a global minimum point for 1.

So, I'm assuming we are trying to optimize $a$, $b$, and $c$ here? Otherwise this is relatively simple to solve for $a$, $b$, and $c$ and then find the minimum given the observations. Not sure how to set up a minimization problem for this?

• Are you famliar with least squares and polynomial regression? Apr 26, 2017 at 6:17
• I solved the problem. Thanks, we had not done anything stats related in the class so far so I wasn't really thinking in those terms till you mentioned it. Apr 26, 2017 at 7:30