Practice #1
Graph the function f(x) = -|x + 1| - 2. State the vertex and describe the translation.
Create your x-y table.
| x | y |
| -3 | -|-3 + 1|- 2 = -|-2| -2 = -2 -2 = -4 |
| -2 | -|-2 + 1|- 2 = -|-1| -2 = -1 -2 = -3 |
| -1 | -|-1 + 1|-2 = -|0| -2 = 0 -2 = -2 |
| 0 | -|0 + 1|-2 = -|1| -2 = -1 -2 = -3 |
| 1 | -|1 + 1|-2 = -|2| -2 = -2 -2 = -4 |
Plot your points and draw your graph.
| x | y | Ordered Pair |
| -3 | -4 | (-3, -4) |
| -2 | -3 | (-2, -3) |
| -1 | -2 | (-1, -2) |
| 0 | -3 | (0, -3) |
| 1 | -4 | (1, -4) |
What is the vertex of the graph?
Is the vertex for the graph a maximum the highest point on a graph or minimum the lowest point on a graph point?
Which of the following best describes the translation from the parent function f(x) = |x|?
1. Flipped over, translated 1 unit right and 4 units down
2. Flipped over, translated 1 unit left and 2 units down
3. Flipped over, translated 1 unit right and 2 units up
4. Translated 1 unit left and 2 units down
Practice #2
Graph the function y = |x - 3| + 4. State the vertex and whether it is a maximum or minimum value and describe the translation.
Complete the table.
| x | y |
| 1 | |1 - 3| + 4 = |-2| + 4 = 2 + 4 = 6 |
| 2 | |2 - 3| + 4 = |-1| + 4 = 1 + 4 = 5 |
| 3 | |3 - 3| + 4 = |0| + 4 = 0 + 4 = 4 |
| 4 | |4 - 3| + 4 = |1| + 4 = 1 + 4 = 5 |
| 5 | |5 - 3| + 4 = |2| + 4 = 2 + 4 = 6 |
Plot your points and draw your graph.
| x | y | Ordered Pair |
| 1 | 6 | (1, 6) |
| 2 | 5 | (2, 5) |
| 3 | 4 | (3, 4) |
| 4 | 5 | (4, 5) |
| 5 | 6 | (5, 6) |
Where is the vertex of the graph?
Is the vertex of the graph a maximum or minimum point?
Describe the translation.
1. 3 units right and 4 units up
2. 4 units right and 3 units up
3. 3 units left and 4 units up
4. 3 units left and 4 units down
