Question: A museum curator uses a quadratic model $ p(y) = y^2 - 6y + 9m $ to estimate the restoration time (in days) of an instrument based on its age $ y $, where $ m $ is a preservation factor. If $ p(5) = 22 $, find $ m $.

Fri, 01 May 2026 10:40:55 +0000

Title: How to Solve for the Preservation Factor $ m $ in a Quadratic Restoration Model Understanding how museums estimate the restoration time of historical instruments is essential for preserving cultural heritage accurately. In this case, a museum curator uses a quadratic model:
$$ p(y) = y^2 - 6y + 9m $$
to predict the time (in days) required to restore an instrument based on its age $ y $. Given that $ p(5) = 22 $, we go through a clear step-by-step solution to find the unknown preservation factor $ m $. --- ### Step 1: Understand the given quadratic model