To sketch the graph of the quadratic function \( y = x^2 - 4x + 4 \), let's break down the key features of the function.

### 1. **Identify the type of function**:
   - The equation \( y = x^2 - 4x + 4 \) is a quadratic function, which means its graph will be a parabola.

### 2. **Rewrite the function in vertex form**:
   - The standard form is \( y = ax^2 + bx + c \). Here, \( a = 1 \), \( b = -4 \), and \( c = 4 \).
   - The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
   - Complete the square to rewrite the function in vertex form:
     \[
     y = x^2 - 4x + 4 = (x - 2)^2
     \]
   - The vertex is \( (2, 0) \).

### 3. **Determine the axis of symmetry**:
   - The axis of symmetry is a vertical line that passes through the vertex. For this function, it's \( x = 2 \).

### 4. **Identify the direction of the parabola**:
   - Since \( a = 1 > 0 \), the parabola opens upwards.

### 5. **Find the y-intercept**:
   - The y-intercept occurs where \( x = 0 \).
   \[
   y = 0^2 - 4(0) + 4 = 4
   \]
   - The y-intercept is \( (0, 4) \).

### 6. **Find the x-intercepts**:
   - The x-intercepts occur where \( y = 0 \).
   \[
   0 = (x - 2)^2
   \]
   - Solve for \( x \): \( x = 2 \).
   - The x-intercept is a double root at \( (2, 0) \), meaning the parabola touches the x-axis at this point.

### 7. **Sketch the graph**:
   - Draw a parabola with the vertex at \( (2, 0) \) and passing through the point \( (0, 4) \).
   - The parabola touches the x-axis at \( (2, 0) \) and opens upwards.

Here is a simple sketch of the graph:

```
y
|
|       *
|     *   *
|    *     *
|   *       *
|  *         *
| *           *
------------------------- x
            (2, 0)
```

### Do you want details or have any questions? Here are 5 related questions to further explore:

1. How do you determine if a quadratic function has a maximum or minimum point?
2. How would the graph change if the coefficient of \( x^2 \) was negative?
3. What is the importance of the discriminant in determining the nature of the roots?
4. How do you find the vertex of a quadratic function using the formula \( -\frac{b}{2a} \)?
5. How can you determine the number of x-intercepts a quadratic function will have?

**Tip:** When sketching graphs of quadratic functions, always start by identifying the vertex, axis of symmetry, and the direction in which the parabola opens. This provides a solid foundation for the rest of the graph.

Learn how to sketch the graph of the quadratic function y = x^2 - 4x + 4. This detailed solution includes identifying the vertex, axis of symmetry, direction of the parabola, and finding intercepts. Suitable for high school students studying quadratic functions and parabolas.

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