Answer:
a = 3, b = -1, c = 2
Step-by-step explanation:
an^2 + bn + c
n = 1:
a + b + c = 4 Eq. 1
n = 2:
4a + 2b + c = 12 Eq. 2
n = 3:
9a + 3b + c = 26 Eq. 3
Eq. 2 minus Eq. 1
3a + b = 8 Eq. 4
Eq. 3 minus Eq. 2
5a + b = 14 Eq. 5
Eq. 5 minus Eq. 4
2a = 6
a = 3
Plug in a = 3 into Eq. 4
3(3) + b = 8
b = -1
Plug in a = 3 and b = -1 into Eq. 1.
3 - 1 + c = 4
c = 2
Answer: a = 3, b = -1, c = 2
