*f*(*x*) = *x*2;

stretch vertically by a factor of 6, shift downward 5 units, and shift 2 units to the right

The given function is \( f(x) = x^2 \). To transform it based on the instructions:

1. **Stretch vertically by a factor of 6:** This multiplies the entire function by 6. The new function becomes \( 6x^2 \).
   
2. **Shift downward by 5 units:** Subtract 5 from the function, so it becomes \( 6x^2 - 5 \).
   
3. **Shift 2 units to the right:** Replace \( x \) with \( (x - 2) \) to shift the function horizontally. The final equation is:

\[
f(x) = 6(x - 2)^2 - 5
\]

This is the transformed function after applying the specified transformations.

Would you like further details or explanations?

### 5 Related Questions:
1. How would a horizontal stretch affect the function?
2. What happens if the function is shifted left instead of right?
3. How does a reflection across the x-axis alter the function?
4. Can you apply multiple transformations in a different order and get the same result?
5. What would happen if the function were shifted upward instead of downward?

### Tip:
When shifting horizontally, replacing \( x \) with \( (x - h) \) moves the graph to the right, and replacing it with \( (x + h) \) moves it to the left.

f(x) = x^2; stretch vertically by a factor of 6, shift downward 5 units, and shift 2 units to the right.

Learn how to transform the quadratic function f(x) = x^2 by applying a vertical stretch, shifting downward by 5 units, and shifting 2 units to the right. Understand the key steps and concepts behind these transformations. Suitable for students in Grades 9-10.

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