Question

Move at least one of the 9 guide points below to complete the graph of y, equals, vertical bar, x, plus, 2, vertical bar, plus, 2y=∣x+2∣+2. Moving the red points changes the vertical stretch or compression. Moving the blue point shifts the function left/right/up/down. Click the buttons below to start over or reflect over the x-axis.

Answer 1

To draw y = |x + 2| + 2, put the vertex at (-2, 2) and make the two arms have slope ±1. Practical steps:

1. Move the blue point (shift) to the vertex: (-2, 2).
2. Move the red/guide points to lie on the V-shaped graph. Nine convenient points are:
- (-6, 6)
- (-5, 5)
- (-4, 4)
- (-3, 3)
- (-2, 2) (vertex)
- (-1, 3)
- ( 0, 4)
- ( 1, 5)
- ( 2, 6)

These satisfy y = |x + 2| + 2 (notice y − 2 = |x + 2|). If you use the reflect-over-x button, the graph will become y = −|x + 2| − 2 (all y-values negated).