Math Gold Medalist

Lor

2022 AMC 12B 

Problem 14

The graph of $y=x^2+2x-15$ intersects the $x$-axis at points $A$ and $C$ and the $y$-axis at point $B$. What is $\tan(\angle ABC)$?

$\textbf{(A) }\frac{1}{7} \qquad \textbf{(B) }\frac{1}{4} \qquad \textbf{(C) }\frac{3}{7} \qquad \textbf{(D) }\frac{1}{2} \qquad \textbf{(E) }\frac{4}{7}$

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   Solution