Select the graph that represents the function: $$ x^{2}-12 x+27 $$

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To analyze the function $$ x^{2} - 12x + 27 $$ and determine its graph, we can follow these steps:

1. **Identify the type of function**: This is a quadratic function in the standard form $$ ax^2 + bx + c $$.

2. **Find the vertex**: The vertex of a quadratic function can be found using the formula $$ x = -\frac{b}{2a} $$.

3. **Determine the direction of the parabola**: Since the coefficient of $$ x^2 $$ (which is $$ a = 1 $$) is positive, the parabola opens upwards.

4. **Calculate the y-intercept**: The y-intercept occurs when $$ x = 0 $$.

5. **Plot key points**: We can calculate a few points to get a better idea of the shape of the graph.

Let's perform these calculations step by step.

First, we will find the vertex. The coefficients are $$ a = 1 $$ and $$ b = -12 $$.

Now, let's calculate the x-coordinate of the vertex:

$$
x = -\frac{-12}{2 \cdot 1} = \frac{12}{2} = 6
$$

Next, we will find the y-coordinate of the vertex by substituting $$ x = 6 $$ back into the function:

$$
y = (6)^2 - 12(6) + 27
$$

Now, let's calculate this value.
Calculate the value by following steps:
- step0: Calculate:
  $$6^{2}-12\times 6+27$$
- step1: Multiply the numbers:
  $$6^{2}-72+27$$
- step2: Evaluate the power:
  $$36-72+27$$
- step3: Calculate:
  $$-9$$
The y-coordinate of the vertex is $$ -9 $$. Therefore, the vertex of the function $$ x^{2} - 12x + 27 $$ is at the point $$ (6, -9) $$.

Next, let's find the y-intercept by substituting $$ x = 0 $$ into the function:

$$
y = (0)^2 - 12(0) + 27 = 27
$$

Now we have two key points:
- Vertex: $$ (6, -9) $$
- Y-intercept: $$ (0, 27) $$

Since the parabola opens upwards, we can sketch the graph based on these points.

Now, let's summarize the characteristics of the graph:
- The vertex is at $$ (6, -9) $$.
- The y-intercept is at $$ (0, 27) $$.
- The parabola opens upwards.

With this information, you can select the graph that matches these characteristics. If you have specific graph options, please provide them, and I can help you identify the correct one.
The graph of the function $$ x^{2} - 12x + 27 $$ is a parabola opening upwards with its vertex at $$ (6, -9) $$ and y-intercept at $$ (0, 27) $$.

Select the graph that represents the function:

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