Question

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

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 $(0,0)$