2025 AMC 10A Problems/Problem 9: Difference between revisions

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

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) more than $4$

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		Let <imath>f(x) = 100x^3 - 300x^2 + 200x</imath>. For how many real numbers <imath>a</imath> does the graph of <imath>y = f(x - a)</imath> pass through the point <imath>(1, 25)</imath>?

		(A) <imath>1</imath> (B) <imath>2</imath> (C) <imath>3</imath> (D) <imath>4</imath> (E) more than <imath>4</imath>