starting at x=0, the 2nd differences are constant (2) so yes, it is a quadratic
y = x^2+3
Determine whether the given table of values represents a quadratic function x= -1 / 0 /1 / 2 / 3
y= 4 / 3 / 4 / 7 / 12
2 answers
The difference between x-values is constant so use differences of y- values to determine the model.
If the second difference is the same value, the model will be quadratic.
First difference of y-values:
3 - 4 = - 1
4 - 3 = 1
7 - 4 = 3
12 - 7 = 5
Second difference of y-values:
1 - ( - 1 ) = 1 + 1 = 2
3 - 1 = 2
5 - 3 = 2
The second difference is the same value, so the given table of values represents a quadratic function.
By the way this quadratic function is:
y = x^2 + 3
If the second difference is the same value, the model will be quadratic.
First difference of y-values:
3 - 4 = - 1
4 - 3 = 1
7 - 4 = 3
12 - 7 = 5
Second difference of y-values:
1 - ( - 1 ) = 1 + 1 = 2
3 - 1 = 2
5 - 3 = 2
The second difference is the same value, so the given table of values represents a quadratic function.
By the way this quadratic function is:
y = x^2 + 3