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The given function is \( g(x) = (x + 4)^2 \), and you are asked to use transformations of the graph of \( f(x) = x^2 \) to determine the graph of \( g(x) \).

### Step-by-Step Transformation:

1. **Starting with the basic function**:
   - The base function is \( f(x) = x^2 \), which is a standard parabola with its vertex at the origin \((0, 0)\) and opens upwards.

2. **Horizontal shift**:
   - The function \( g(x) = (x + 4)^2 \) involves a horizontal shift. When we add a value inside the parentheses like this (\( x + 4 \)), it causes a horizontal shift to the left by 4 units.
   - This means the vertex of the parabola, which was originally at \( (0, 0) \), will now be at \( (-4, 0) \).

3. **Shape and orientation**:
   - The shape of the graph of \( g(x) \) remains the same as \( f(x) = x^2 \). It is still a parabola opening upwards since the coefficient of \( (x + 4)^2 \) is positive.
   - There is no vertical stretch, compression, or reflection involved here, as the equation remains \( (x + 4)^2 \).

### Summary:
- The graph of \( g(x) = (x + 4)^2 \) is a parabola that has been shifted 4 units to the left from the graph of \( f(x) = x^2 \). The vertex of the new parabola is at \( (-4, 0) \).

Would you like further details on this transformation or have any questions?

Here are some follow-up questions that might help expand your understanding:
1. How would the graph change if the equation was \( g(x) = (x - 4)^2 \)?
2. What would happen if the equation included a vertical shift, like \( g(x) = (x + 4)^2 + 2 \)?
3. How does a negative coefficient, such as \( g(x) = -(x + 4)^2 \), affect the graph?
4. How can you determine the axis of symmetry of the function \( g(x) = (x + 4)^2 \)?
5. What is the effect of adding a coefficient in front of the squared term, such as \( g(x) = 2(x + 4)^2 \)?

**Tip**: Horizontal shifts always move the graph in the opposite direction of the sign inside the function. For example, \( x + 4 \) shifts left, and \( x - 4 \) shifts right.

Use transformations of the graph of f(x) = x^2 to determine the graph of the given function g(x) = (x + 4)^2.

Explore how the graph of f(x) = x^2 can be transformed to g(x) = (x + 4)^2 using horizontal shifts. Understand the step-by-step transformation process and the resulting vertex shift for students in Grades 9-11.

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