https://file.aiquickdraw.com/mathbot/file/1730594298579tfyr2nx0.jpg

To transform the solid black function \( y = -x^2 \) to match the dotted function, we need to identify the transformations required. The dotted function is a vertically shifted version of the solid black parabola.

Here's the process to match the dotted function:

1. **Vertical Shift**: The dotted function seems to be moved downwards by a certain amount compared to the original.
2. **Transformation**: To shift the graph vertically, we modify the function by adding a constant \( c \) at the end of the function. The transformation should look like:
   \[
   y = -(x)^2 + c
   \]
   where \( c \) is a negative number to shift the graph down.

Estimate the value of \( c \) by comparing the positions of the vertices of the two parabolas.

Would you like a deeper explanation of function transformations?

### Relative Questions
1. How do vertical shifts affect the graph of a function?
2. What happens when we add or subtract inside the function \( f(x) \) rather than outside?
3. How would a horizontal shift impact this graph?
4. What is the impact of changing the coefficient of \( x^2 \) in a quadratic function?
5. How do you determine the direction of a parabola?

### Tip
To match functions visually, try moving along the x or y directions in small steps, observing the graph's alignment as you go.

Transform the solid black function \( y = -x^2 \) to match the dotted function shown in the image.

Learn how to transform a quadratic function by applying a vertical shift to match a target function. This example covers transformations of the function \( y = -x^2 \), with a detailed explanation of vertical shifts. Suitable for students in Grades 9-10.

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