Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.
\(A(a,a^2)\\ B(b,b^2)\\ \dfrac{b^2-a^2}{b-a}=2\\ \dfrac{(b+a)(b-a)}{b-a}=2\)
\(\color{blue}b+a=2\\ \)
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+1234 
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