How do you graph #y = -abs(x + 4)#?

Question

Hazel Anglin · Accepted Answer

This is an upside-down V shape with arms having slope #+-1# and vertex at #(-4, 0)#

#abs(x+4) = x+4# when #x+4 >= 0#, that is when #x >= -4# So #y = -abs(x+4) = -x-4# has slope #-1# when #x >= -4#

#abs(x+4) = -(x+4)# when #x+4 < 0#, that is when #x < -4# So #y = -abs(x+4) = x+4# has slope #1# when #x < -4#

The vertex is at the point where #(x+4) = 0#, giving #x = -4# and #y = 0#. So the vertex is at #(-4, 0)#

The intersection with the #y# axis will be where #x=0#. Substituting #x=0# into the equation, we get #y = -abs(4) = -4#. So the intersection is at #(0, -4)#

graph{-abs(x+4) [-13.38, 6.62, -5.84, 4.16]}

Abigail Allen · Answer

undefined To graph the equation $ y = -|x + 4| $, follow these steps:

1. Identify the vertex of the absolute value function, which is the point where the absolute value function intersects the x-axis. In this case, the vertex is at (-4, 0).

2. Plot the vertex on the coordinate plane.

3. Determine the direction of the graph. Since the coefficient of the absolute value function is negative (-1), the graph will be reflected across the x-axis.

4. Plot additional points on both sides of the vertex. Substitute values of x into the equation to find corresponding y-values. Choose values to the left and right of the vertex for symmetry.

5. Connect the points with a smooth curve, reflecting the graph across the x-axis.

Following these steps, you will obtain the graph of $ y = -|x + 4| $.