Find the quadratic function that fits the data points (1,6) (-1,2) and (3,34).
Equation of a PARABOLA: y = ax2 + bx + c
6 = a(1)2 + b(1) + c ----- Substituting (1, 6) for (x, y)
6 = a + b + c ---- eq (i)
y = ax2 + bx + c
2 = a(- 1)2 + b(- 1) + c ----- Substituting (- 1, 2) for (x, y)
2 = a - b + c ---- eq (ii)
y = ax2 + bx + c
34 = a(3)2 + b(3) + c ----- Substituting (3, 34) for (x, y)
34 = 9a + 3b + c ---- eq (iii)
6 = a + b + c ------ eq (i)
2 = a - b + c ------ eq (ii)
34 = 9a + 3b + c --- eq (iii)
4 = 2b ---- Subtracting eq (ii) from eq (i)
32 = 8a + 4b ----- Subtracting eq (ii) from eq (iii) ---- eq (iv)
32 = 8a + 4(2) --- Substituting 2 for b in eq (iv)
6 = 3 + 2 + c ---- Substituting 3 for a, and 2 for b in eq (i)
6 = 5 + c
1 = c
Equation of a PARABOLA: y = ax2 + bx + c
y = 3x2 + 2x + 1 ------- Substituting 3 for a, 2 for b, and 1 for c