we have
[tex]y=-x^2-6x+16[/tex]
using a graph tool
see the attached figure
The vertex of the quadratic equation is the point [tex](-3,25)[/tex]
That means that the maximum height of an arch is equal to [tex]25\ units[/tex]
The zeroes of the function are the points [tex](-8,0)\ and\ (2,0)[/tex]
That means that the width of the arch at its base is equal to difference between the zeroes
[tex]=(2-(-8))=2+8=10\ units[/tex]
therefore
the answer is
The width of the arch at its base is equal to the difference between the zeroes
