Consider the quadratic graph y = (x+3)2+6.

To translate the graph upwards by 2 units, the required function can be expressed as Answer field  

To translate the graph leftwards by 2 units, the required function can be expressed as Answer field  


To translate the graph rightwards by 2 units, the required function can be expressed as Answer field  


To translate the graph downwards by 2 units, the required function can be expressed as Answer field  

To modify the graph of \( y = (x + 3)^2 + 6 \), different transformations (vertical and horizontal) can be applied as follows:

1. **To translate the graph upwards by 2 units**: 
   \[
   y = (x + 3)^2 + 6 + 2 = (x + 3)^2 + 8
   \]

2. **To translate the graph leftwards by 2 units**: 
   \[
   y = \left( (x + 3) + 2 \right)^2 + 6 = (x + 5)^2 + 6
   \]

3. **To translate the graph rightwards by 2 units**: 
   \[
   y = \left( (x + 3) - 2 \right)^2 + 6 = (x + 1)^2 + 6
   \]

4. **To translate the graph downwards by 2 units**: 
   \[
   y = (x + 3)^2 + 6 - 2 = (x + 3)^2 + 4
   \]

These transformations directly modify the constants associated with the graph's position.

Would you like further details on these transformations or have any questions?

Here are 5 related questions:
1. How would you translate the graph by 2 units diagonally (both left and down)?
2. How does translating a graph horizontally differ from translating it vertically?
3. What effect would multiplying the quadratic by a constant have on the graph?
4. How would a reflection over the x-axis affect the equation?
5. How would the equation change if you wanted to stretch the graph vertically by a factor of 2?

**Tip:** When translating horizontally, modifying \( x \) inside the parentheses affects the left-right movement, while adjusting constants outside affects vertical shifts.

Consider the quadratic graph y = (x+3)^2 + 6. To translate the graph upwards by 2 units, the required function can be expressed as Answer field. To translate the graph leftwards by 2 units, the required function can be expressed as Answer field. To translate the graph rightwards by 2 units, the required function can be expressed as Answer field. To translate the graph downwards by 2 units, the required function can be expressed as Answer field.

Learn how to translate the quadratic graph y = (x+3)^2 + 6 upwards, downwards, leftwards, and rightwards. This guide walks through essential graph transformations using vertical and horizontal shifts. Suitable for students in Grades 9-10.

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