1. **State the problem:** We are given the function $$f(x) = -0.3 (x - 2)^2 + 4$$ which models height in feet as a function of distance in feet. We know the point $(0, 2.8)$ lies on the graph and want to find the unknown $x$-coordinate where the height is $1.3$, i.e., find $x$ such that $$f(x) = 1.3.$$ 2. **Write the equation to solve:** Set the function equal to 1.3: $$-0.3 (x - 2)^2 + 4 = 1.3.$$ 3. **Isolate the squared term:** Subtract 4 from both sides: $$-0.3 (x - 2)^2 = 1.3 - 4 = -2.7.$$ 4. **Divide both sides by -0.3:** $$(x - 2)^2 = \frac{-2.7}{-0.3} = 9.$$ 5. **Take the square root of both sides:** $$x - 2 = \pm 3.$$ 6. **Solve for $x$:** - If $x - 2 = 3$, then $x = 5$. - If $x - 2 = -3$, then $x = -1$. 7. **Interpretation:** The parabola reaches height 1.3 at two distances: $x = -1$ feet and $x = 5$ feet. **Final answer:** The unknown $x$-coordinates are $$x = -1 \text{ and } x = 5.$$