Question

Use y = 16x^2 to complete the table. What pattern (symmetry) do you notice from the table?

Answer 1

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:

$\left[\begin{array}{cccccccccccccccc}x&-4&-3&-2.5&-2&-1.5&-1&-0.5&0&0.5&1&1.5&2&2.5&3&4\\y&240&\end{array}\right]$

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:

$\left[\begin{array}{cccccccccccccccc}x&-4&-3&-2.5&-2&-1.5&-1&-0.5&0&0.5&1&1.5&2&2.5&3&4\\y&240&144&100&64&36&16&4&0&4&16&36&64&10&144&240\end{array}\right]$

Then we can see that there is a symmetry around the value x = 0.