Question

Complete the table.

f(d) = 7d2 + 7d − 3
d f(d)
–3
–2
–1
0

Answer 1

To complete the table for the function \( f(d) = 7d^2 + 7d - 3 \), we will calculate the value of \( f(d) \) for each value of \( d \).

1. For \( d = -3 \):
\[
f(-3) = 7(-3)^2 + 7(-3) - 3
\]
\[
= 7(9) - 21 - 3
\]
\[
= 63 - 21 - 3
\]
\[
= 39
\]

2. For \( d = -2 \):
\[
f(-2) = 7(-2)^2 + 7(-2) - 3
\]
\[
= 7(4) - 14 - 3
\]
\[
= 28 - 14 - 3
\]
\[
= 11
\]

3. For \( d = -1 \):
\[
f(-1) = 7(-1)^2 + 7(-1) - 3
\]
\[
= 7(1) - 7 - 3
\]
\[
= 7 - 7 - 3
\]
\[
= -3
\]

4. For \( d = 0 \):
\[
f(0) = 7(0)^2 + 7(0) - 3
\]
\[
= 0 + 0 - 3
\]
\[
= -3
\]

Now we can fill in the table:

\[
\begin{array}{|c|c|}
\hline
d & f(d) \\
\hline
-3 & 39 \\
-2 & 11 \\
-1 & -3 \\
0 & -3 \\
\hline
\end{array}
\]