Tables

Tables

Example 3

Find the equation that models this table in vertex form.

x

-2

-1

0

1

2

3

4

y

12

9

7

6

6

7

9

Step 1 . Find the second difference.

x

-2

-1

0

1

2

3

4

y

12

9

7

6

6

7

9

TablesEx3-1
Step 2. Find the a-value.

The a-value is found by dividing the second difference by 2.

TablesEx2-2

Step 3. Find the h-value.

The h-value is the x-coordinate of the vertex. Due to symmetry, the x-coordinate of the vertex is 1.5. Therefore, h = 1.5.

Step 4. Find the k-value.

Substitute a and h into the equation and solve for k.

TablesEx3-3

Step 5 . Substitute a, h and k into the equation.

TablesEx3-4