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.
Note that the difference between consecutive x-values is always 1 — it is constant.
Additionally, the consecutive y-values have a second difference of - 4. This means that the table represents a quadratic function. Let's recall the intercept form of this type of function.
y=a(x-p)(x-q)
We can see in the table that there is only one x-intercept, p=q=0. Using this intercept, we can write a partial equation of the function represented by the table.
y=a(x-0)(x-0) ⇔ y=ax^2
To find the value of a, we will substitute the ordered pair (1,- 2) in the above equation.
