Copy and complete the table of value and draw the graph of $$ y=x^{2}+3 x-1 $$ $$ | $$\begin{tabular}{c|c|c|c|c|c|c|c|}$$ x $$ & -3 & -2 & -1 & 0 & 1 & 2 & 3 \ $$ y $$ & 35 & 4 \ \hline\end{tabular}

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To complete the table of values for the function $$ y = x^2 + 3x - 1 $$, we will calculate the value of $$ y $$ for each $$ x $$ in the table.

1. For $$ x = -3 $$:
   $$
   y = (-3)^2 + 3(-3) - 1 = 9 - 9 - 1 = -1
   $$

2. For $$ x = -2 $$:
   $$
   y = (-2)^2 + 3(-2) - 1 = 4 - 6 - 1 = -3
   $$

3. For $$ x = -1 $$:
   $$
   y = (-1)^2 + 3(-1) - 1 = 1 - 3 - 1 = -3
   $$

4. For $$ x = 0 $$:
   $$
   y = (0)^2 + 3(0) - 1 = 0 + 0 - 1 = -1
   $$

5. For $$ x = 1 $$:
   $$
   y = (1)^2 + 3(1) - 1 = 1 + 3 - 1 = 3
   $$

6. For $$ x = 2 $$:
   $$
   y = (2)^2 + 3(2) - 1 = 4 + 6 - 1 = 9
   $$

7. For $$ x = 3 $$:
   $$
   y = (3)^2 + 3(3) - 1 = 9 + 9 - 1 = 17
   $$

Now we can fill in the table:

$$
\begin{tabular}{c|c|c|c|c|c|c|c|}
$$ x $$ & -3 & -2 & -1 & 0 & 1 & 2 & 3 \ 
\hline
$$ y $$ & -1 & -3 & -3 & -1 & 3 & 9 & 17 \ 
\hline
\end{tabular}
$$

### Graphing the Function

To graph the function $$ y = x^2 + 3x - 1 $$, we can plot the points from the completed table:

- $$ (-3, -1) $$
- $$ (-2, -3) $$
- $$ (-1, -3) $$
- $$ (0, -1) $$
- $$ (1, 3) $$
- $$ (2, 9) $$
- $$ (3, 17) $$

The graph will be a parabola opening upwards, as the coefficient of $$ x^2 $$ is positive.

You can plot these points on a coordinate plane and draw a smooth curve through them to represent the function. The vertex of the parabola can also be found using the vertex formula $$ x = -\frac{b}{2a} $$ where $$ a = 1 $$ and $$ b = 3 $$:

$$
x = -\frac{3}{2(1)} = -\frac{3}{2} = -1.5
$$

Substituting $$ x = -1.5 $$ back into the equation will give the $$ y $$-coordinate of the vertex.

This completes the table and provides the necessary information to graph the function.
Complete the table with the following values for $$ y $$: -3, -3, -1, 3, 9, 17. The graph is a parabola opening upwards with the vertex at $$ x = -1.5 $$.

Copy and complete the table of value
and draw the graph of

-3 -2 -1 0 1 2 3

35 4

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Copy and complete the table of value and draw the graph of -3 -2 -1 0 1 2 3 35 4