1. **Problem Statement:** We are given a graph that starts near $y=6$ at $x=0$, decreases sharply to $y=0$ near $x=1$, rises to a peak near $y=2.5$ at $x=2$, then falls again to $y=0$ near $x=3$, and remains at $y=0$ for $x$ beyond 3 up to 4. 2. **Goal:** Find a formula that fits this behavior. 3. **Observations:** - The graph touches $y=0$ at $x=1$ and $x=3$. - It starts high at $x=0$ and ends at $y=0$ for $x>3$. - The shape suggests a polynomial with roots at $x=1$ and $x=3$. 4. **Assuming a polynomial form:** $$y = a(x-1)^2(x-3)^2$$ This form ensures zeros at $x=1$ and $x=3$ with multiplicity 2, creating the peaks and valleys. 5. **Find coefficient $a$ using $y(0) = 6$:** $$6 = a(0-1)^2(0-3)^2 = a(1)^2(3)^2 = 9a$$ $$a = \frac{6}{9} = \frac{2}{3}$$ 6. **Final formula:** $$y = \frac{2}{3}(x-1)^2(x-3)^2$$ This formula matches the given graph's key points and shape.