Table of values represent a QUADRATIC FUNCTION OR NOT

Answer the following if the given table of values represent a QUADRATIC FUNCTION or NOT

x -3 -2 -1 0 1 2 3
f(x) 18 8 2 0 2 8 18

x -3 -2 -1 0 1 2 3

f(x) 18 8 2 0 2 8 18

yes

Did you plot the points and not notice they look like a parabola?

To determine if a table of values represents a quadratic function, you need to check if the values follow a consistent pattern or trend that can be described by a quadratic equation.

Here are the steps to determine if a table of values represents a quadratic function:

Step 1: Examine the x-values
Check if the x-values in the table are increasing or decreasing at a consistent rate. If the x-values are increasing or decreasing by a constant amount, it suggests a linear function rather than a quadratic function.

Step 2: Find the differences between consecutive y-values
Calculate the differences between consecutive y-values. If the differences are the same, it indicates a linear function. However, if the differences are not the same, proceed to the next step.

Step 3: Find the differences between the differences of y-values
Calculate the differences between the differences of the y-values. If these differences are constant, it suggests a quadratic function. In other words, if the second differences are the same, the table of values represents a quadratic function.

Step 4: Construct a quadratic equation
If the table of values passes the previous steps and is determined to represent a quadratic function, you can construct the quadratic equation. Use the general form of a quadratic equation: y = ax^2 + bx + c. Substitute values from the table to solve for the coefficients a, b, and c. If the equation can accurately represent all the values in the table, it confirms that the table represents a quadratic function.

By following these steps, you can determine if a table of values represents a quadratic function or not.