1. The problem describes a parabola with points labeled a, b, and c, where c is the vertex, b is on the same y-coordinate as the dock but on the opposite side of the parabola, and a is near the boat. 2. To analyze this, we use the vertex form of a parabola equation: $$y = a(x - h)^2 + k$$ where $(h,k)$ is the vertex. 3. Since c is the vertex, its coordinates are $(h,k)$. 4. Point b has the same y-coordinate as the dock, so if the dock is at $y = d$, then $y_b = d$. 5. Because b is on the opposite side of the parabola from a, and the parabola is symmetric about the vertical line $x = h$, the x-coordinates of a and b are equidistant from $h$ but on opposite sides. 6. This symmetry means if $x_b = h + m$, then $x_a = h - m$ for some $m$. 7. Using the vertex form, the y-values at a and b are equal: $$y_a = y_b = a(m)^2 + k$$ 8. This confirms the parabola's symmetry and the relationship between points a, b, and c. Final answer: The parabola is symmetric about the vertical line through vertex c, with points a and b equidistant horizontally from c and sharing the same y-coordinate as the dock.