<s>[INST] The price of a house in a certain area over five years is modeled by the function:
\[f(t) = a + b(t - c)^2\]
where \(t\) is the number of years after 2010 and \(f(t)\) is the price of the house in thousands of dollars.
Given that \(f(1) = 180\), \(f(2) = 200\), and \(f(5) = 300\), solve for \(a\), \(b\), and \(c\).[/INST]