Question

How do you determine if a relation is quadratic by calculation differences, analyzing a graph, examining the degree in an equation

Answer 1

1) We can determine by the table of values whether a function is a quadratic one by considering this example:

x | y 1st difference 2nd difference

0 0 3 -0 = 3 7-3 = 4

1 3 10 -3 = 7 11 -7 = 4

2 10 21 -10 =11 15 -11 = 4

3 21 36-21 = 15 19-5 = 4

4 36 55-36= 19

5 55

2) Let's subtract the values of y this way:

3 -0 = 3

10 -3 = 7

21 -10 = 11

36 -21 = 15

55 -36 = 19

Now let's subtract the differences we've just found:

7 -3 = 4

11-7 = 4

15-11 = 4

19-15 = 4

So, if the "second difference" is constant (same result) then it means we have a quadratic function just by analyzing the table.

3) Hence, we can determine if this is a quadratic relation calculating the second difference of the y-values if the second difference yields the same value. The graph must be a parabola and the highest coefficient must be 2