2022 SSMO Relay Round 2 Problems/Problem 2

Problem

Let $T=TNYWR$ . Suppose that the monic quadratic $f(x)$ is tangent to the function $g(x)=|x+2|-T$ at two points, when graphed on the coordinate plane. Then $|f(1)|$ can be expressed as $\frac mn$ , where $m$ and $n$ are relatively prime positive integers. Find $10m+n$ .

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2022 SSMO Relay Round 2 Problems/Problem 2

Problem

Solution