Identify the two tables which represent quadratic relationships

Option (4) and Option (5)

Step-by-step explanation:

By calculating the second difference, if the second difference in a table is equal, table will represent the quadratic relationship.

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

x             y             Ist difference         IInd difference

0            4                      -                                             -

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

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

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

Second difference of the terms in y are the same as 8.

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

Similarly, in Option (5) we will calculate the second difference of y terms.

x            y            Ist difference     IInd 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 is same as 2.

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

d

step-by-step explanation:

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13