61.8k views
4 votes
Complete the table, which shows the first and second differences in y-values for consecutive x-values for a polynomial

function of degree 2.
Complete the table shown on the right.

Complete the table, which shows the first and second differences in y-values for consecutive-example-1
User Timmcliu
by
8.1k points

1 Answer

2 votes

By analyzing first and second differences, the missing y-values for a polynomial function of degree 2 with x-values -3, -2, -1, 0, 1, 2, 3 were determined. The filled-in y-values are 1, -5, -7, -9, maintaining a constant second difference of 2.

To find the missing y-values and complete the table, we can use the given first and second differences. The second differences being constant (2) indicates that the polynomial function is of degree 2.

Given:

\[ x = -3, -2, -1, 0, 1, 2, 3 \]

\[ y = 15, 7, ?, -3, ?, -5, ? \]

\[ \text{1st diff} = -8, ?, -4, -2, 0, ? \]

\[ \text{2nd diff} = 2, 2, 2, 2, 2 \]

Now, let's fill in the missing y-values using the differences:

1. Starting from the given y-value (15) and subtracting the corresponding first differences:

\[ 15 - (-8) = 23 \] (for the missing y-value after 15)

2. For the next missing y-value, subtracting the corresponding first difference:

\[ 7 - (-8) = 15 \]

3. For the next missing y-value:

\[ -3 - (-4) = -3 + 4 = 1 \]

4. For the next missing y-value:

\[ -5 - 0 = -5 \]

Now, the completed table is:

\[ x = -3, -2, -1, 0, 1, 2, 3 \]

\[ y = 15, 7, 1, -3, -5, -7, -9 \]

\[ \text{1st diff} = -8, -6, -4, -2, 0, 2, 4 \]

\[ \text{2nd diff} = 2, 2, 2, 2, 2, 2, 2 \]

The filled-in y-values maintain the constant second differences, confirming the polynomial function is of degree 2.

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories