https://file.aiquickdraw.com/mathbot/file/17255999063399t6pyxq0.jpg

The image you uploaded contains a function \( f(x) = -0.5x^2 + 1 \) and a partially filled-in chart with graphing details, such as domain, range, intercepts, and increasing/decreasing intervals. Below, I'll walk through the problem step-by-step, providing explanations for each component of the function and the requested details.

### 1. **Parent Function**:
The given function is a quadratic function \( f(x) = -0.5x^2 + 1 \), so its parent function is:
\[ f(x) = x^2 \]
This is a standard parabola that opens upward, with the vertex at \( (0, 0) \).

### 2. **Transformations**:
There are two transformations applied to the parent function:
- **Vertical Compression**: The coefficient \( -0.5 \) compresses the graph vertically by a factor of 0.5 and reflects it over the x-axis.
- **Vertical Shift**: The constant term \( +1 \) shifts the graph upward by 1 unit.

### 3. **Graphing**:
The graph is a downward-facing parabola due to the negative coefficient. The vertex of the parabola is at \( (0, 1) \), which comes from the transformation of the parent function.

### 4. **Domain**:
The domain of a quadratic function is all real numbers:
\[ \text

Given the quadratic function f(x) = -0.5x^2 + 1, fill in the details such as domain, range, intercepts, and increasing/decreasing intervals.

Explore the quadratic function f(x) = -0.5x^2 + 1, including its domain, range, intercepts, and increasing/decreasing intervals. Learn about transformations, such as vertical compression and shifts. Ideal for students in Grades 9-11.

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