The shape of an archway is modelled by the graph of a quadratic function. The maximum height of the archway is $4 \mathrm{m}$ and the maximum width is $4 \mathrm{m}$. The graph shows a model of the archway.

Find a function to model the archway.

Use the function to determine whether an object $3 \mathrm{m}$ wide and $1.6 \mathrm{m}$ tall will fit through the archway.