Okay, now I see the sixth and final problem. The instruction is to translate the given parabola "6 units up". The original graph is a downward-opening parabola with its vertex at (0, -4). To solve this, I need to shift every point on this parabola vertically by 6 units upwards. This means the new vertex will be at (0, -4 + 6), which is (0, 2), and every other point on the curve will also move up by 6 units. I have now analyzed all six problems.
To summarize the solution for each problem:
1.
Problem 1: 3 units up
* Original vertex: (0, 0)
* New vertex: (0, 3)
*
Solution: Draw an upward-opening parabola with its vertex at (0, 3).
2.
Problem 2: 2 units down
* Original vertex: (0, 1)
* New vertex: (0, -1)
*
Solution: Draw a downward-opening parabola with its vertex at (0, -1).
3.
Problem 3: 5 units left
* Original vertex: (1, -2)
* New vertex: (-4, -2)
*
Solution: Draw a downward-opening parabola with its vertex at (-4, -2).
4.
Problem 4: 1 unit right
* Original vertex: (-2, -3)
* New vertex: (-1, -3)
*
Solution: Draw an upward-opening parabola with its vertex at (-1, -3).
5.
Problem 5: 4 units down
* Original vertex: (0, 2)
* New vertex: (0, -2)
*
Solution: Draw an upward-opening parabola with its vertex at (0, -2).
6.
Problem 6: 6 units up
* Original vertex: (0, -4)
* New vertex: (0, 2)
*
Solution: Draw a downward-opening parabola with its vertex at (0, 2).
The task is to draw these new graphs on the provided coordinate planes. The key is to identify the vertex of the original parabola and then apply the horizontal or vertical shift to find the new vertex. The shape and orientation of the parabola remain unchanged; only its position moves.
Parent Tip: Review the logic above to help your child master the concept of function transformation worksheet.
