Answer
See graph
Work Step by Step
1. Draw the x and y axes of the coordinate system. The origin (0, 0) represents the point where the cables touch the roadway.
2. Draw a horizontal line segment that represents the roadway. This line segment should be centered at the origin and extend $640$ units to either side.
3. Draw two vertical line segments that represent the towers. Each tower is $152$ meters above the roadway, so these line segments should be $152$ units long and centered at $(0, 152)$ and $(1280, 152)$.
4. Draw a curve that represents the shape of the cables. The cables follow the shape of a parabola, with the lowest point at the origin and the highest point at the midpoint between the towers. To draw the curve, you can use the equation of a parabola in standard form: $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola and a determines the shape of the curve. In this case, the vertex is at $(640, 0)$ and a is a negative number that depends on the length of the cables and the distance between the towers.
5. Label the coordinates of the known points on the graph. These points are $(0, 0)$, $(0, 152)$, $(640, 0)$, $(640, 152)$, and $(1280, 152)$.
