Calculate the difference and ratio between consecutive terms. Is either of these the same throughout the sequence?
Model That Best Describes the Data: Quadratic Equation: y=3x^2
Practice makes perfect
Finding the Model
We want to identify which kind of model best describes the data, linear, quadratic or exponential. To do so we will calculate the difference and ratio between consecutive terms.
x
0
1
2
3
4
y
0
3
12
27
48
Let's begin by calculating the first differences.
The first differences are not all equal. Therefore, the table of values does not represent a linear function. Let's find the second differences and compare them.
Since the second differences are all equal, the table of values represents a quadratic function.
Finding the Equation
Let's recall the general form of this type of function.
y=ax^2
We will use one ordered pair given in the table to find the value of a. For simplicity, let's use (1,3). We will start by substituting 1 and 3 for x and y respectively.
