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2025 AMC 10AProblem 9P1-10~4 minPrint
FunctionsPolynomialsBound the quantity above/below or estimate to pin it downSubstitute to simplify (u = x+1/x, shifting, scaling)

Let f(x)=100x3−300x2+200xf(x) = 100x^3 - 300x^2 + 200x . For how many real numbers aa does the graph of y=f(x−a)y = f(x - a) pass through the point (1,25)(1, 25) ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.