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.