Question

Identify the two tables which represent quadratic relationships. x 0 1 2 3 y -4 -8 -10 -10 x 0 1 2 3 y 4 -4 -4 4 x 0 1 2 3 y -2 0 2 4 x 0 1 2 3 y 1 2 4 8 x 0 1 2 3 y -2 -4 -8 -16 x 0 1 2 3 y 3 4 5 6

Answer 1

To estimate that table given in Option (4) will define the quadratic relationship.

Therefore, the table of Option (5) will describe the quadratic relationship.

How to estimate the quadratic relationships between two tables?

By estimating the second difference, if the second difference in a table exists equivalent, the table will define the quadratic relationship.

In the given option, we estimate that table given in Option (4) will define the quadratic relationship.

x       y      I st difference       II nd difference

0      4           -                               -

1      -4      -4 - (4) = -8                    -  

2     -4      -4 - (-4) = 0                0 - (-8) = 8

3      4       4 - (-4) = 8                 8 - 0 = 8

The second difference between the terms in y exists exactly as 8.

Therefore, the table of Option (4) means the quadratic relationship.

Similarly, in Option (5) we will estimate the second distinction of y terms.

x        y             I st difference       II nd difference

0      -4                     -                          -

1       -8               -8 - (-4) = -4              -

2     -10             -10 - (-8) = -2      -2 - (-4) = 2  

3     -10             -10 - (-10) = 0       0 - (-2) = 2

Here the second difference exists identical to 2.

Therefore, the table of Option (5) will describe the quadratic relationship.

To learn more about quadratic equations refer to:

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