Question 108620
Yes, you can connect the dots.
Graphing the points you see that it is a parabola opening downward. 
{{{ graph( 300, 300, -4, 16, -10, 40, 30.25-(x-5.5)^2) }}}
The x coordinate of the vertex (maximum value) is midpoint between 5 and 6 or 5.5.
The equation has the form 
{{{A-k=a(L-h)^2}}}
where (h,k) are the (x,y) coordinates of the vertex. 
We need to solve for a and k. 
Use two values for (L,A) that you have: (10,10) and (9,18)
{{{A-k=a(L-5.5)^2}}}
{{{10-k=a(10-5.5)^2}}}
1.{{{10-k=20.25a}}}
{{{18-k=a(9-5.5)^2}}}
2.{{{18-k=12.25a}}}
Subtracting eq.2 from eq. 1 gives
{{{10-k-(18-k)=20.25a-12.25a}}}
{{{-8=8a}}}
{{{a=-1}}}
Using that value in 1.
1.{{{10-k=20.25a}}}
{{{10-k=20.25(-1)}}}
{{{k=20.25+10}}}
{{{k=30.25}}}
Your equation then becomes
{{{A-k=a(L-h)^2}}}
{{{A-30.25=-(L-5.5)^2}}} or
{{{A=30.25-(L-5.5)^2}}}
Check your answers. 
A(10)= 10
A(9) = 18
A(8) = 24 
A(7) = 28 
A(6) = 30
A(5) = 30
A(4) = 28
A(3) = 24
A(2) = 18
A(1) = 10