1. The problem states that $f(x) = ax^2 + 2x - 11$ and the point $(1, 0)$ lies on the graph of $f$. This means when $x = 1$, $f(x) = 0$. 2. Substitute $x = 1$ and $f(1) = 0$ into the function: $$0 = a(1)^2 + 2(1) - 11$$ 3. Simplify the equation: $$0 = a + 2 - 11$$ $$0 = a - 9$$ 4. Solve for $a$: $$a = 9$$ Therefore, the value of $a$ is 9.