Look for a pattern in each table of values to determine which model best describes the data. Then write an equation for tue function that models the data.
X: -1, 0, 1, 2, 3
Y: 6, 0, 6, 24, 54
If you divide the y-values by 6, you get the sequence
-1 0 1 2 3
1 0 1 4 9
Look familiar?
To determine which model best describes the data, we can start by looking for a pattern in the table of values.
Let's examine the relationship between the x-values and the y-values:
When x = -1, y = 6
When x = 0, y = 0
When x = 1, y = 6
When x = 2, y = 24
When x = 3, y = 54
From observing the table, we can see that the relationship between x and y is not linear since the y-values do not increase or decrease by a constant rate for each increase in x. However, we can notice that there seems to be a relation between the values of y and x^2.
Let's calculate the square of each x-value:
(-1)^2 = 1
(0)^2 = 0
(1)^2 = 1
(2)^2 = 4
(3)^2 = 9
Now, let's compare the original y-values with the square of each x-value:
y = 6, x^2 = 1
y = 0, x^2 = 0
y = 6, x^2 = 1
y = 24, x^2 = 4
y = 54, x^2 = 9
We can see that the y-values are equal to 6 times the square of each corresponding x-value. Therefore, the relationship between x and y can be described by the equation:
y = 6x^2
So, the function that models the given data is y = 6x^2.