Question 1003299
the average height of a castle door bounded by the parabola {{{y = 4 -x^2}}} and the x-axis

parabola {{{y = 4 -x^2}}} or {{{y = -x^2+4}}} has negative sign in front of {{{x^2}}}, so {{{a<0}}} and parabola opens downwards 

then the vertex is its maximum which is at  {{{4-0^2 = 4}}} or at point ({{{ 0}}},{{{4}}})

the average height of a castle door bounded by the parabola will be equal to {{{y}}} coordinate of the vertex which is {{{4}}} units above {{{x}}} axis


{{{drawing( 600, 600, -10, 10, -10, 10,
line(0.1,0,0.1,4),
 graph( 600, 600, -10, 10, -10, 10, 4 -x^2)) }}}