Question 1203474
<pre>

{{{drawing(400,2400/11,-11,11,-1,11,
circle(1,8,.2),locate(1,9,"(1,8)"),
graph(400,2400/11,-11,11,-1,11,((-8/99)x^2+800/99)*(sqrt(10-x)/sqrt(10-x))*(sqrt(10+x)/sqrt(10+x)) )    )}}}

Put the base on the x-axis and the axis of symmetry on the y-axis
and let each unit be 1 foot.  Then it has x-intercepts at (10,0) and 
(-10,0) and passes through the point (1,8).

We could use the vertex form of a parabola, but since I don't know which
vertex form you've studied, I'll use the general form:

Its equation is 

{{{y}}}{{{""=""}}}{{{ax^2+bx+c}}}

Substitute the three points it passes through:

{{{system(0=a*10^2+b*10+c, 8=a*1^2+b*(1)+c, 0=a*(-10)^2+b*(-10)+c)}}}

Simplify:

{{{system(100a+10b+c=0,a+b+c=8,100a-10b+c=0)}}}

Subtract the third equation from the first equation and get
{{{20b=0}}}
{{{b=0}}}

{{{system(100a+c=0,a+c=8,100a+c=0)}}}

Then a = 8-c

100a + c = 0
100(8-c) + c = 0
800-100c + c = 0
800-99c = 0
-99c = -800
   c = 800/99 

a = 8-c
a = 8-800/99 = -8/99

So the equation of the parabola is

{{{y=expr(-8/9)x^2+800/99}}}

So the height at the center is when x=0 or 800/99 or 8.08080808... feet.

Edwin</pre>