Sketch the graph of the pair of functions. Use a dashed line for g(x).

f(x) = x2 , g(x) = - (1/4)(x + 3)2 + 4

To sketch the graphs of the functions \( f(x) = x^2 \) and \( g(x) = -\frac{1}{4}(x + 3)^2 + 4 \), follow these steps:

### Step 1: Analyze \( f(x) = x^2 \)
This is a standard parabola that opens upwards with the vertex at the origin (0,0). Key features include:
- **Vertex**: (0, 0)
- **Axis of symmetry**: The y-axis (x = 0)
- **Shape**: Symmetric and upwards, passing through points like (-1, 1), (1, 1), (-2, 4), (2, 4), etc.

### Step 2:

Sketch the graph of the pair of functions. Use a dashed line for g(x). f(x) = x^2 , g(x) = - (1/4)(x + 3)^2 + 4

Learn how to sketch the graphs of the quadratic functions f(x) = x^2 and g(x) = - (1/4)(x + 3)^2 + 4. This step-by-step guide includes an analysis of transformations, vertices, and symmetry. Suitable for students in Grades 9-11.

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Solution

Step 1: Analyze $f(x) = x^2$

Step 2:

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