In the $xy$-plane, the graph of   $y=x^2+2x+a$   contains the points $(-1,0 )$ and $(2,b)$. What is the value of $b$?

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We first substitute the point with known $x$ and $y$ coordinates to find the value of $a$:

$$y=x^2+2x+a$$ $$0=(-1)^2+2(-1)+a$$ $$0=1-2+a$$ $$0=-1+a$$ $$1=a$$ We obtain the full equation and use the other point to find $b$. $$y=x^2+2x+1$$ $$b=(2)^2+2(2)+1$$ $$b=4+4+1$$ $$b=\boxed{9}$$