so I 'think' I understand what your after the data is a bit mismatched tho. how about this...

$\displaystyle f(x)=a(x-h)^2+k$

a=the number that stretches the parabola. values under 1 flatten it out.

x=your input value 1,2,3,4...

h=the shift of the vertex(ie. lowest or highest point) of the parabola left or right.

k=the shift up or down of the parabola.

so if you want the highest y values at (7,1.267) the h=-7 k=1.267.

now to flatten out the curve to match your data set a=-0.04 or something like that. if your interested in x DOMAIN 2...13. remember the range is y values.

so you get $\displaystyle f(x)=-0.04(x-7)^2+1.267$

once you expand and collect you get $\displaystyle f(x)=-0.04x^2+0.56x-0.693$

does this even remotely help you? fiddle with h,k,a in standard form then expand into general form if you need to. altho your not going to turn a line into a parabola and have your values match up all that well.

if you want something that is linear that goes to a target value then back down linear use a absolute value function

Absolute value - Wikipedia, the free encyclopedia