Given that y = 7 + 3x − x², complete the table below and draw the graph of y = 7 + 3x − x².

a) To complete the table, substitute each value of $x$ into the equation $y = 7 + 3x - x^2$.

For $x = -2$:

$$y = 7 + 3(-2) - (-2)^2 = 7 - 6 - 4 = -3$$

For $x = -1$:

$$y = 7 + 3(-1) - (-1)^2 = 7 - 3 - 1 = 3$$

For $x = 2$:

$$y = 7 + 3(2) - (2)^2 = 7 + 6 - 4 = 9$$

For $x = 3$:

$$y = 7 + 3(3) - (3)^2 = 7 + 9 - 9 = 7$$

For $x = 4$:

$$y = 7 + 3(4) - (4)^2 = 7 + 12 - 16 = 3$$

For $x = 5$:

$$y = 7 + 3(5) - (5)^2 = 7 + 15 - 25 = -3$$

The completed table is:

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline y & -11 & -3 & 3 & 7 & 9 & 9 & 7 & 3 & -3 & -11 \\ \hline \end{array}$$

b) To draw the graph of $y = 7 + 3x - x^2$:

1. Draw and label the x-axis and y-axis on the provided grid.
2. Choose a suitable scale for both axes. For example, 1 cm to represent 1 unit on the x-axis and 1 cm to represent 2 units on the y-axis. Ensure the scale accommodates x-values from -3 to 6 and y-values from -11 to 9.
3. Plot the points from the completed table: $(-3, -11)$, $(-2, -3)$, $(-1, 3)$, $(0, 7)$, $(1, 9)$, $(2, 9)$, $(3, 7)$, $(4, 3)$, $(5, -3)$, $(6, -11)$.
4. Draw a smooth curve connecting all the plotted points. This curve will be a parabola opening downwards.