AMC 12 2006b Problem 12

The parabola $y=ax^2+bx+c$ has vertex $(p,p)$ and $y$-intercept $(0,-p)$, where $p\ne 0$. What is $b$?

$\text {(A) } -p \text {(B) } 0 \text {(C) } 2 \text {(D) } 4 \text {(E) } p$