Answer:
y = x² + 1
Explanation:
Consider the differences in the y values
y : 1 2 5 10 17
1 3 5 7 ← first differences are not constant so not linear
Consider the differences of the first differences
1 3 5 7
2 2 2← second differences are constant
Because the second differences are constant the relationship is quadratic
The form of the relationship is
y = x² ± c ← where c is a constant
Substitute values of x into the relationship to find what is needed
x = 0 : y = 0² = 0 ← require to add 1 to obtain 1
x = 1 : y = 1² = 1 ← require to add 1 to obtain 2
x = 2 : y = 2² = 4 ← require to add 1 to obtain 5
x = 3 : y = 3² = 9 ← require to add 1 to obtain 10
x = 4 : y = 4² = 16 ← require to add 1 to obtain 17
Hence relationship is y = x² + 1