Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

Let f : [$-$1, 1] $\to$ R be defined as f(x) = ax² + bx + c for all x$\in$[$-$1, 1], where a, b, c$\in$R such that f($-$1) = 2, f'($-$1) = 1 for x$\in$($-$1, 1) the maximum value of f ''(x) is ${{1 \over 2}}$. If f(x) $\le$ $\alpha$, x$\in$[$-$1, 1], then the least value of $\alpha$ is equal to _________.