Explicit Equations For Quadratic Sequences

Question

I cannot figure out how to write explicit equations for quadratic sequences. The sequence is 9, 6, 5, 6, 9. If i’m correct the rate of change is positive 2. Please help me figure out how to write it. The zero term is 5. (Does not need to be in standard form)

Answer 1

You could start with a standard form of quadratic:

f(x) = ax² + bx + c

f(0) = 5, therefore c = 5

f(1) = 6, so a + b + 5 = 6

f(2) = 9, so 4a + 2b + 5 = 9

You should be able to solve those simultaneous equations for a and b