The function f(x)=−5(x+4)2+3  contains the following transformations:

It flips over the         [ Select ]      ["", "x", "y", ""]  -axis.

It has a vertical stretch of         [ Select ]      ["5", "4", "3"]  units.

It shifts horizontally         [ Select ]      ["5", "3", "4"]  units to the         [ Select ]      ["left", "right"] 

It shifts vertically         [ Select ]      ["3", "4", "5"]  units         [ Select ]      ["down", "up"] 

Let’s analyze the transformations step by step for the given function: 

### Given Function:  
\( f(x) = -5(x+4)^2 + 3 \)

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### 1. **Reflection (Flip over an axis):**  
The negative sign outside the leading coefficient (\(-5\)) reflects the graph over the **x-axis**.  

- **Answer:** **x-axis**

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### 2. **Vertical Stretch:**  
The coefficient \(-5\) represents a vertical stretch by a factor of **5**.  

- **Answer:** **5**

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### 3. **Horizontal Shift:**  
The term \( (x + 4) \) means the function shifts **4 units** **to the left**. The "+" inside the parentheses indicates movement to the left.

- **Answer:** **4 units to the left**

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### 4. **Vertical Shift:**  
The constant \( +3 \) outside the quadratic term shifts the graph **3 units up**.  

- **Answer:** **3 units up**

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### Final Answer Summary:
1. It flips over the **x-axis**.  
2. It has a vertical stretch of **5** units.  
3. It shifts horizontally **4 units to the left**.  
4. It shifts vertically **3 units up**.

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Would you like me to expand further on any of the transformations?  

### Related Questions:
1. What is the vertex of this transformed parabola?  
2. How does the vertical stretch affect the steepness of the graph?  
3. What would happen if the coefficient \(-5\) were changed to \(+5\)?  
4. Can you write the transformation if the function were \( f(x) = 2(x-1)^2 - 6 \)?  
5. How do you determine if a parabola opens upwards or downwards?

### Tip:  
To easily identify horizontal shifts, look at the **opposite sign** inside the parentheses with \(x\).

The function f(x) = −5(x+4)^2 + 3 contains the following transformations: It flips over the [ Select ] ["", "x", "y", ""]-axis. It has a vertical stretch of [ Select ] ["5", "4", "3"] units. It shifts horizontally [ Select ] ["5", "3", "4"] units to the [ Select ] ["left", "right"]. It shifts vertically [ Select ] ["3", "4", "5"] units [ Select ] ["down", "up"].

Learn how to analyze the transformations of the quadratic function f(x) = −5(x+4)^2 + 3. This includes reflection over the x-axis, vertical stretch, horizontal and vertical shifts. Suitable for students in Grades 9-12.

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