Question 373074
(0,-2)(1,-1)(2,2)(3,7)
 
we could use a polynomial : P(x)=ax^3+bx^2+cx-2
 
P(0) = -2
P(1) = a + b + c - 2 = -1
P(2) = 8a + 4b + 2c - 2 = 2
P(3) = 27a + 9b + 3c -2 = 7
 
a + b + c = 1
8a + 4b + 2c = 4
27a + 9b + 3c = 9
 
2*(1)-(2) and 3(1)-(3) gives : 
 
-6a - 2b = -2 | times 4
-24a - 6b = -6
 
-2b = -2 => b = 1
 
-6a = -2 + 2 = 0 => a = 0

c = 1 - a - b = 1 - 1 = 0
 
 The polynomial is : P(x) = x^2 - 2
 
 
Check : 
P(1) = 1 - 2 = -1
P(2) = 4 - 2 = 2
P(3) = 9 - 2 = 7

{{{ graph( 300, 200, -1, 4, -2, 10,  x^2 - 2) }}}