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

Second differences: 11,13,15,17 → constant second difference 2 = 2a, so a = 1.

With a = 1, use x = 4: 21 = 16 + 4b + c → 4b + c = 5.
Use x = 5: 32 = 25 + 5b + c → 5b + c = 7. Subtract → b = 2.
Then c = 5 − 4b = 5 − 8 = −3.

So c = −3.