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The image contains the following problem based on transformations of the function \( f(x) = x^2 \):

**Problem**:
Starting with the graph of \( f(x) = x^2 \), write the equation of the graph that results from:

**(a)** Writing \( f(x) \) 3 units upwards:  
\[ y = \_\_\_\_\_ \]

**(b)** Shifting \( f(x) \) 2 units to the left:  
\[ y = \_\_\_\_\_ \]

**(c)** Reflecting \( f(x) \) about the x-axis:  
\[ y = \_\_\_\_\_ \]

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### Solutions:

1. **(a) Writing \( f(x) \) 3 units upwards**:  
   To shift a function \( f(x) \) upwards by \( k \) units, you add \( k \) to the function:  
   \[
   y = f(x) + 3 = x^2 + 3
   \]
   
2. **(b) Shifting \( f(x) \) 2 units to the left**:  
   To shift a function \( f(x) \) left by \( h \) units, you replace \( x \) with \( x + h \):  
   \[
   y = f(x + 2) = (x + 2)^2
   \]

3. **(c) Reflecting \( f(x) \) about the x-axis**:  
   To reflect a function \( f(x) \) about the x-axis, you multiply the function by \( -1 \):  
   \[
   y = -f(x) = -x^2
   \]

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Would you like further details on transformations or have any questions about these steps? Here are 5 related questions:

1. How would you shift \( f(x) \) by 4 units to the right?
2. What would the equation be if \( f(x) \) was reflected over the y-axis instead of the x-axis?
3. How do you vertically stretch \( f(x) = x^2 \) by a factor of 2?
4. How can we reflect \( f(x) \) over both the x-axis and the y-axis?
5. What happens to the graph when you shift it both horizontally and vertically?

**Tip**: When shifting graphs, always check whether the shift is horizontal or vertical, as each type has a different effect on the equation.

Starting with the graph of f(x) = x^2, write the equation of the graph that results from: (a) writing f(x) 3 units upwards, (b) shifting f(x) 2 units to the left, and (c) reflecting f(x) about the x-axis.

Explore how to transform the quadratic function f(x) = x^2 by shifting it vertically, moving it horizontally, and reflecting it across the x-axis. Understand the effects of each transformation with clear examples. Perfect for students in Grades 9-11.

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