Function Help?

Question

Hi! I'm stuck on this function problem!
X Y
1 3
2 6
3 11
Thanks!!! I give best answers!!! :) -ry

Answer 1

Are you trying to find a binomial of x?

y(x) = a*x^2 + b*x + c?

3 = a + b +c (1)
6 = 4*a + 2*b+c (2)
11 = 9*a + 3*b + c (3)

(2) - (1) : 3 = 3a + b (4)
(3) - (2): 5 = 5a + b (5)

(5) - (4) : 2 = 2a => a = 2/2 = 1;

=> (1) <=> 3 = 1 + b + c or 2 = b + c (6)
(2) <=> 6 = 4 + 2b +c or 2 = 2b+c (7)

(7) - (6) : 0 = b => b = 0

(6) <=> 2 = 0 + c => c = 2

a = 1
b = 0
c = 2

y(x) = x^2 + 2
Rechecks:
y(1) = 1 + 2 = 3
y(2) = 2^2 +2 = 4 +2 = 6
y(3) = 3^2 + 2 = 9 +2 = 11
All are correct!

Answer 2

Y = X^2 + 2

Answer 3

Y = X^2 + 2 :))

Answer 4

What is the question?

If the question is to find a formula for f(x) that fits all three points, here is one:

f(x) = 3 + 3(x-1) + (x-1)(x-2)

You can check that f(1) = 3, f(2) = 6, f(3) = 11.

This was solved using Newton's forward difference formula.

Answer 5

f(x)=x^2 + 2

Make a table of values for x & x^2 to see the pattern.

Answer 6

(1,3)
(2,6)
(3,11)

y= x^2+2

3=1^2+2
6=2^2+2
11=3^2+2