Question

The table shows some values of a function of the form y = ax2 + bx + c.
x- 4, 5 ,6, 7, 8
y- 21 , 32 , 45 , 60 , 77

The value of c, the constant of the function, is
.

Answer 1

c = -3

Reason: Second differences are constant 2, so a = 2/2 = 1. Then y = x^2 + bx + c. Using x=4: 21 = 16 + 4b + c, and x=5: 32 = 25 + 5b + c. Subtracting gives b = 2, then c = 21 - 16 - 4(2) = -3.