b = -4.5 (slider from -10 to 10, step 0.5)
f(x) = -(0.5) * x^(2.0) + b * x + 1.0
P: (b, (b^(2.0) + 2.0) / 2.0)
A1 = 2.5
B1 = 4.125
A2 = 2
B2 = 3
A3 = 1.5
B3 = 2.125
A4 = 1
B4 = 1.5
A5 = 0.5
B5 = 1.125
A6 = 0
B6 = 1
A7 = -0.5
B7 = 1.125
A8 = -1
B8 = 1.5
A9 = -1.5
B9 = 2.125
A10 = -2
B10 = 3
A11 = -2.5
B11 = 4.125
A12 = -3
B12 = 5.5
A13 = -3.5
B13 = 7.125
A14 = -4
B14 = 9
A15 = -4.5
B15 = 11.125