Question

Determine whether the given table of values represents a quadratic function x= -1 / 0 /1 / 2 / 3
y= 4 / 3 / 4 / 7 / 12

Answer 1

starting at x=0, the 2nd differences are constant (2) so yes, it is a quadratic
y = x^2+3

Answer 2

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