Determining the Quadratic Function from a Table | Step-by-Step Guide and Example

Which quadratic function is represented by the table?

To determine the quadratic function represented by a table, we need to examine the pattern of the data points and use it to find the equation of the quadratic function

To determine the quadratic function represented by a table, we need to examine the pattern of the data points and use it to find the equation of the quadratic function. The general form of a quadratic function is given by:

f(x) = ax^2 + bx + c

where a, b, and c are constants.

Let’s consider an example table:

| x | y |
|—|—|
| 1 | 4 |
| 2 | 7 |
| 3 | 10 |
| 4 | 13 |
| 5 | 16 |

To find the quadratic function that matches this table, we need to find the values of a, b, and c.

Step 1: Finding the value of a:
To find the value of a, we look at the constant differences in the y-values. In this case, the differences are always 3. This suggests that the coefficient of x^2 (a) is 3/2 (half of the common difference).

Step 2: Finding the value of b:
To find the value of b, we need to analyze the linear term. As the difference between the y-values is constant, we can see that there is a linear term with a coefficient of 1. Therefore, the coefficient of x (b) is 1.

Step 3: Finding the value of c:
To find the value of c, we can substitute the values of x and y from any point in the table into the quadratic function. Let’s use the first point (1, 4):
4 = (3/2)(1^2) + 1(1) + c
4 = (3/2) + 1 + c
4 = 3/2 + 2/2 + c
4 = 5/2 + c
c = 4 – 5/2
c = 8/2 – 5/2
c = 3/2

Therefore, the quadratic function represented by the table is:
f(x) = (3/2)x^2 + x + 3/2

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