#### $\frac{4}{5}$Question: An angel investor models the growth of two startups' valuations with $ f(x) = x^2 - 3x + m $ and $ g(x) = x^2 - 3x + 5m $. If $ f(2) = g(2) $, determine $ m $.

February 22, 2026

$#### $\frac{4}{5}$Question: An angel investor models the growth of two startups' valuations with $ f(x) = x^2 - 3x + m $ and $ g(x) = x^2 - 3x + 5m $. If $ f(2) = g(2) $, determine $ m $.$

$\frac{9}{25} + \cos^2 \theta = 1$
$\cos^2 \theta = 1 - \frac{9}{25} = \frac{16}{25}$
$\cos \theta = \sqrt{\frac{16}{25}} = \frac{4}{5}$ (positif dans le premier quadrant)
Solution: Set $ f(2) = g(2) $. Compute $ f(2) = 4 - 6 + m = -2 + m $ and $ g(2) = 4 - 6 + 5m = -2 + 5m $. Equate: $ -2 + m = -2 + 5m $. Simplify: $ 0 = 4m $, so $ m = \boxed{0} $.
Question: A chemist designs a catalyst where the reaction efficiency is modeled by $ h(x) = x^2 - 4x + m $. If the efficiency at $ x = 3 $ equals the efficiency of a second catalyst $ k(x) = x^2 - 4x + 2m $ at $ x = 1 $, find $ m $.
Solution: Compute $ h(3) = 9 - 12 + m = -3 + m $ and $ k(1) = 1 - 4 + 2m = -3 + 2m $. Set equal: $ -3 + m = -3 + 2m $. Simplify: $ 0 = m $, so $ m = \boxed{0} $.

#### \(\frac{4}{5}\)Question: An angel investor models the growth of two startups' valuations with $ f(x) = x^2 - 3x + m $ and $ g(x) = x^2 - 3x + 5m $. If $ f(2) = g(2) $, determine $ m $.

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