Question

The table shows some values of a function of the form y = ax2 + bx + c.

x= 2 3 4 5 6 7
y= 17 32 53 80 113 157

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

Answer 1

Using x = 2, 3, 4:
4a + 2b + c = 17
9a + 3b + c = 32
16a + 4b + c = 53

Subtracting gives 5a + b = 15 and 7a + b = 21, so 2a = 6 ⇒ a = 3, then b = 15 − 5a = 0. Plugging into 4a + 2b + c = 17 gives 12 + c = 17 ⇒ c = 5.

So c = 5.