1. The problem is to generalize the equation $h = -5(t-2)^2 + 20$. 2. This equation is in vertex form of a quadratic function: $$h = a(t - h)^2 + k$$ where $(h, k)$ is the vertex and $a$ determines the parabola's direction and width. 3. In the given equation, $a = -5$, $h = 2$, and $k = 20$. 4. To generalize, replace constants with variables: $$h = a(t - h)^2 + k$$ where $a$, $h$, and $k$ are any real numbers. 5. This general form represents any parabola with vertex at $(h, k)$ and vertical stretch/compression and reflection determined by $a$. Final generalized equation: $$h = a(t - h)^2 + k$$