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When Function C is decreasing, is Function D increasing or decreasing?

The image shows two functions, Function C and Function D. Function C appears to be a parabola that opens upwards, which means it represents a quadratic function. 

For a quadratic function like this, the function is decreasing on the left side of the vertex and increasing on the right side.

Function D is shown to be \( f(x) = -x^2 \), which is also a quadratic function but opens downwards.

### Analysis:
- **Function C** is decreasing as \( x \) moves from left to right until it reaches the vertex.
- **Function D** (which is \( f(x) = -x^2 \)) decreases as \( x \) moves away from the vertex in both directions (left and right).

**Answer**: When Function C is decreasing (which happens to the left of the vertex), Function D is also decreasing.

Would you like more details, or do you have any further questions? Here are some related questions you might find interesting:

1. What is the vertex of Function C and how do you find it?
2. What is the vertex of Function D, given the equation \( f(x) = -x^2 \)?
3. How do the domains and ranges of Functions C and D compare?
4. What would happen to Function D if the coefficient of \( x^2 \) were positive?
5. How can you determine the axis of symmetry for a quadratic function?

**Tip**: For quadratic functions, the vertex is a key point that determines where the function changes from decreasing to increasing or vice versa.

Explore the relationship between two quadratic functions, Function C and Function D, and how their behavior changes. Understand when Function C decreases, Function D also decreases, based on their respective forms and properties. Suitable for high school students studying quadratic functions.

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