Answer:
In the table, we can see values of x and y, to complete it, we just need to input the different values of x in the equation:
y = 16*x^2
For example in the first slot, we have x = -4
Then we will have:
y = 16*(-4)^2 = 240
Then we complete the empty slot with 240.
The table would be:
[tex]\left[\begin{array}{cccccccccccccccc}x&-4&-3&-2.5&-2&-1.5&-1&-0.5&0&0.5&1&1.5&2&2.5&3&4\\y&240&\end{array}\right][/tex]
Now we just need to do the same for the other values:
y(-3) = 16*(-3)^2 = 144
y(-2.5) = 16*(-2.5)^2 = 100
y(-2) = 16*(-2)^2 = 64
y(-1.5) = 16*(-1.5)^2 = 36
y(-1) = 16*(-1)^2 = 16
y(-0.5) = 16*(-0.5)^2 = 4
y(0) = 16*(0)^2 = 0
y(0.5) = 16*(0.5)^2 = 4
y(1) = 16*(1)^2 = 16
y(1.5) = 16*(1.5)^2 = 36
y(2) = 16*(2)^2 = 64
y(2.5) = 16*(2.5)^2 = 100
y(3) = 16*(3)^2 = 144
y(4) = 16*(4)^2 = 240
Then the complete table is:
[tex]\left[\begin{array}{cccccccccccccccc}x&-4&-3&-2.5&-2&-1.5&-1&-0.5&0&0.5&1&1.5&2&2.5&3&4\\y&240&144&100&64&36&16&4&0&4&16&36&64&10&144&240\end{array}\right][/tex]
Then we can see that there is a symmetry around the value x = 0.
