Draw the graph of $$ f(x)=9(x+4)^{2}+3 $$

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To graph the function $$ f(x) = 9(x + 4)^2 + 3 $$, we can follow these steps:

1. **Identify the Vertex**: The function is in the vertex form of a quadratic equation, which is $$ f(x) = a(x - h)^2 + k $$. Here, $$ a = 9 $$, $$ h = -4 $$, and $$ k = 3 $$. Thus, the vertex of the parabola is at the point $$ (-4, 3) $$.

2. **Determine the Direction**: Since $$ a = 9 $$ is positive, the parabola opens upwards.

3. **Find the Axis of Symmetry**: The axis of symmetry is the vertical line that passes through the vertex, which is $$ x = -4 $$.

4. **Calculate Additional Points**: To get a better idea of the shape of the graph, we can calculate a few additional points by choosing values of $$ x $$ around the vertex.

- For $$ x = -5 $$:
     $$
     f(-5) = 9(-5 + 4)^2 + 3 = 9(-1)^2 + 3 = 9 + 3 = 12
     $$
     So, the point is $$ (-5, 12) $$.

- For $$ x = -3 $$:
     $$
     f(-3) = 9(-3 + 4)^2 + 3 = 9(1)^2 + 3 = 9 + 3 = 12
     $$
     So, the point is $$ (-3, 12) $$.

- For $$ x = -6 $$:
     $$
     f(-6) = 9(-6 + 4)^2 + 3 = 9(-2)^2 + 3 = 9(4) + 3 = 36 + 3 = 39
     $$
     So, the point is $$ (-6, 39) $$.

- For $$ x = -2 $$:
     $$
     f(-2) = 9(-2 + 4)^2 + 3 = 9(2)^2 + 3 = 9(4) + 3 = 36 + 3 = 39
     $$
     So, the point is $$ (-2, 39) $$.

5. **Plot the Points**: Now we can plot the points we have:
   - Vertex: $$ (-4, 3) $$
   - Points: $$ (-5, 12) $$, $$ (-3, 12) $$, $$ (-6, 39) $$, $$ (-2, 39) $$

6. **Draw the Parabola**: Connect the points with a smooth curve to form the parabola.

### Summary of Key Points:
- Vertex: $$ (-4, 3) $$
- Opens upwards
- Axis of symmetry: $$ x = -4 $$
- Additional points: $$ (-5, 12) $$, $$ (-3, 12) $$, $$ (-6, 39) $$, $$ (-2, 39) $$

This will give you a clear graph of the function $$ f(x) = 9(x + 4)^2 + 3 $$.
To graph $$ f(x) = 9(x + 4)^2 + 3 $$, identify the vertex at $$ (-4, 3) $$, note the upward opening, and plot additional points like $$ (-5, 12) $$, $$ (-3, 12) $$, $$ (-6, 39) $$, and $$ (-2, 39) $$. Connect these points to form the parabola.

Draw the graph of

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