How do the consecutive terms relate to each other?
Type of Function: Quadratic Function: y=5x^2
Practice makes perfect
Finding the Model
We want to tell whether the table of values represents a linear, exponential, or quadratic function. To do so, we will analyze how the consecutive terms are related to each other.
x
-5
-4
-3
-2
-1
y
125
80
45
20
5
Let's begin with 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 values 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 values of a. For simplicity, let's use (-1,5). We will start by substituting -1 and 5 for x and y respectively.
