The graph of f(x)=x^2 is given below. Write the equation of a function h(x) which would first shift the graph to the right 6 units then reflect it over the y-axis

To find the equation of the function \( h(x) \) based on the transformation steps applied to \( f(x) = x^2 \), follow these two steps:

1. **Shift the graph of \( f(x) \) to the right by 6 units**:  
   Shifting a graph horizontally to the right by \( c \) units is done by replacing \( x \) with \( x - c \). In this case, \( c = 6 \). So, the equation becomes:
   \[
   f(x) = (x - 6)^2
   \]

2. **Reflect the graph over the y-axis**:  
   Reflecting a graph over the y-axis is done by replacing \( x \) with \( -x \). Applying this transformation to \( (x - 6)^2 \), the equation becomes:
   \[
   h(x) = (-x - 6)^2
   \]

Thus, the equation of the transformed function is:
\[
h(x) = (-x - 6)^2
\]

Would you like further clarification on how transformations work or any other details?

### Related Questions:
1. What is the effect of shifting a graph left or right on the function's equation?
2. How would you reflect a graph over the x-axis instead of the y-axis?
3. How does a vertical shift affect the function \( f(x) \)?
4. What transformations preserve the shape of the graph of a function?
5. Can multiple transformations be combined into one equation?

### Tip:
Always perform horizontal transformations (shifts and reflections) before vertical ones to avoid confusion.

The graph of f(x)=x^2 is given below. Write the equation of a function h(x) which would first shift the graph to the right 6 units then reflect it over the y-axis.

Learn how to transform the graph of f(x)=x^2 by first shifting it to the right by 6 units and then reflecting it over the y-axis. This step-by-step explanation covers key concepts in transformations and quadratic functions. Suitable for students in Grades 9-12.

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