How do you find the x intercept of #y = -|x+10|#?

1 Answer
Apr 3, 2016

Answer:

The x intercept of a function always occurs when y = 0. Therefore, we must solve the equation for x.

Explanation:

#0 = -|x + 10|#

When solving an absolute value equation, you must consider two scenarios.

a) The absolute value is positive

#0 = -x - 10#

#10 = -x#

#-10 = x#

b) The absolute value is negative

#0 = -(-(x + 10)))#

#0 = -(-x - 10)#

#0 = x + 10#

#-10 = x#

So, there is only 1 x intercept in this case. Here is a graph of your function:

graph{y = -|x + 10| [-20.27, 20.28, -10.14, 10.13]}

However, we must always check. In many cases, there will be more than one x intercept.

Example:

Find the x intercept(s) of #y = |2x + 6| - 4#.

a) The absolute value is #color(red)(+)#:

#0 = 2x + 6 - 4#

#-2 = 2x#

#-1 = x#

b) The absolute value is #color(blue)(-)#

#0 = -(2x + 6) - 4#

#4 = -2x - 6#

#10 = -2x#

#-5 = x#

Thus, we have two x intercepts: #(-1, 0) and (-5, 0)#, as shows the graph of that function.

graph{y = |2x + 6| - 4 [-20.27, 20.28, -10.14, 10.13]}

Practice exercises:

  1. Indicate all the x intercepts of the functions below.

a) #y = |-2x + 7| #

b) #y = |3x - 4| - 3#

c) #y = |5x + 1| + 2x#

Good luck!