a = 0.7 (slider from -3 to 3, step 0.1)
b = 0.6 (slider from -5 to 5, step 0.1)
c = 2.2 (slider from -9 to 9, step 0.1)
f(x) = If[x  <  -1, (a * x^(2)) + c, (-x^(2)) + (b * x)]
P: (-1, f(-1))
Q: (-1, a + c)
g(x) = If[x  <  (-c), sin(x), If[x  <  c, x, x - x^(3) / 6]]
Pg1: ((-c), sin((-c)))
Pg2: ((-c), (-c))
Pg3: (c, c)
Pg4: (c, c - c^(3) / 6)