Complete the tables of values for the following equations: c. y = x2 − 3, d. y = x2 − 5, e. y = 2x2 + 1, f. y = 2x2 − 1

For $x = -3$: $y = (-3)^2 - 3 = 9 - 3 = 6$
For $x = -1$: $y = (-1)^2 - 3 = 1 - 3 = -2$
For $x = 0$: $y = (0)^2 - 3 = 0 - 3 = -3$
For $x = 2$: $y = (2)^2 - 3 = 4 - 3 = 1$
For $x = 4$: $y = (4)^2 - 3 = 16 - 3 = 13$

The completed table is:

$$\begin{array}{|c|c|c|c|c|c|} \hline x & -3 & -1 & 0 & 2 & 4 \\ \hline y & \textbf{6} & \textbf{-2} & \textbf{-3} & \textbf{1} & \textbf{13} \\ \hline \end{array}$$

(Assuming the missing $x$ values are 1 and 3 to complete the table pattern.)
For $x = -4$: $y = (-4)^2 - 5 = 16 - 5 = 11$
For $x = -1$: $y = (-1)^2 - 5 = 1 - 5 = -4$
For $x = 0$: $y = (0)^2 - 5 = 0 - 5 = -5$
For $x = 1$: $y = (1)^2 - 5 = 1 - 5 = -4$
For $x = 3$: $y = (3)^2 - 5 = 9 - 5 = 4$

The completed table is:

$$\begin{array}{|c|c|c|c|c|c|} \hline x & -4 & -1 & 0 & 1 & 3 \\ \hline y & \textbf{11} & \textbf{-4} & \textbf{-5} & \textbf{-4} & \textbf{4} \\ \hline \end{array}$$

For $x = -6$: $y = 2(-6)^2 + 1 = 2(36) + 1 = 72 + 1 = 73$
For $x = -5$: $y = 2(-5)^2 + 1 = 2(25) + 1 = 50 + 1 = 51$
For $x = 0$: $y = 2(0)^2 + 1 = 0 + 1 = 1$
For $x = 5$: $y = 2(5)^2 + 1 = 2(25) + 1 = 50 + 1 = 51$
For $x = 6$: $y = 2(6)^2 + 1 = 2(36) + 1 = 72 + 1 = 73$

The completed table is:

$$\begin{array}{|c|c|c|c|c|c|} \hline x & -6 & -5 & 0 & 5 & 6 \\ \hline y & \textbf{73} & \textbf{51} & \textbf{1} & \textbf{51} & \textbf{73} \\ \hline \end{array}$$

(Assuming the missing $x$ values are 1 and 2 to complete the table pattern.)
For $x = -2$: $y = 2(-2)^2 - 1 = 2(4) - 1 = 8 - 1 = 7$
For $x = -1$: $y = 2(-1)^2 - 1 = 2(1) - 1 = 2 - 1 = 1$
For $x = 0$: $y = 2(0)^2 - 1 = 0 - 1 = -1$
For $x = 1$: $y = 2(1)^2 - 1 = 2(1) - 1 = 2 - 1 = 1$
For $x = 2$: $y = 2(2)^2 - 1 = 2(4) - 1 = 8 - 1 = 7$

The completed table is:

$$\begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline y & \textbf{7} & \textbf{1} & \textbf{-1} & \textbf{1} & \textbf{7} \\ \hline \end{array}$$