Simplifying Composite Functions

For a function $f$, we can denote $f^{\circ n}(x) = f(f(f(f(\dots f(x)\dots))))$, applying $f$ a total of $n$ times. This means that $f^{\circ 1}(x) = f(x)$, $f^{\circ 2}(x) = f(f(x))$, $f^{\circ 3}(x) = f(f(f(x)))$, and so on. $$$$ If $f(x) = x^2 + 3x - 8$, what is $f^{\circ 274}(1)$?