1.1. The graph below shows the curve $y=f(x)$ where $f(x)=5-\frac{{x}^{2}}{6}$.

The curve is to be used as the model for the arch on a bridge where the water level under the bridge is represented by the x-axis. All measurements are in meters.

Write down the maximum height of the bridge above the water.

1.2. Is the bridge wide enough to span a river of width 11 m?

1.3. A second bridge is modelled by the curve $y=f(x)$ where $f(x)=4-\frac{{x}^{2}}{8}$. To support the bridge the arch will continue 2 m under the water (ground) level.

Find the distance between the base of the arch on either side of the river.