Question

1. What is the graph of the absolute value equation? y=|x|-9

2. What is the graph of the absolute value equation?y=|x+4|
3.WHat is the graph of the absolute value equation? y=|x+3|-4
4. What is the graph of the absolute value equation? y= -1/2 |x|

Answer 1

The graph of y = |x| - 9 is V shaped with vertex at (0, -9).

The graph of y = |x + 4| is V shaped with vertex at (-4, 0).

The graph of y = |x + 3| - 4 is V shaped with vertex at (-3, -4).

The graph of y = -1/2|x| is V shaped with vertex at (0, 0)

Answer 2

Using a graphing tool

We're proceeding to graph each of the cases

case 1)
`y=\left|x\right|-9`

The graph in the attached figure N
`1`

The vertex of the graph is the point
`(0,-9)`

The x-intercepts are the points
`(-9,0)` and
`(9,0)`

case 2)
`y=\left|x+4\right|`

The graph in the attached figure N
`2`

The vertex of the graph is the point
`(-4,0)`

The y-intercept is the point
`(0,4)`

case 3)
`y=\left|x+3\right|-4`

The graph in the attached figure N
`3`

The vertex of the graph is the point
`(-3,-4)`

The y-intercept is the point
`(0,-1)`

The x-intercepts are the points
`(-7,0)` and
`(1,0)`

case 4)
`y=-0.5\left|x\right|`

The graph in the attached figure N
`4`

The vertex of the graph is the point
`(0,0)`