#APL NARS, 37 chars

    {(a b n k)←⍵⋄l←n÷⍨b-a⋄+/l×⍺⍺a+l×k+⍳n}

The function has the argument in the left the function, in the right numeric argument a b n k.
In the question k=left here it means k=¯1; k=right here it means k=0. Test:

      f←{(a b n k)←⍵⋄l←n÷⍨b-a⋄+/l×⍺⍺a+l×k+⍳n}
      {1+2×⍵} f 5 13 4 0
    168
      {√⍵} f 1 2.5 3 ¯1
    1.819479217
      {4+(¯3×⍵)+0.2×⍵×⍵} f 12.5 2.5 10 0
    55.5
      {9+(¯4×⍵)+7÷⍨2×⍵×⍵} f 0 15 3 ¯1
    13.57142857
      {6-0×⍵} f 1 4 2 0
    18
      {1+(165×⍵)+⍵*7} f 7 7 4 ¯1
    0
      {⍵×1○÷⍵} f 0 1 50 0
    0.3857239529