How do you solve the absolute value equation y=-2abs(5x+8)+4 and find the vertex, x intercepts and y intercept?

1 Answer
May 28, 2015

Given y = -2abs(5x+8)+4
If (5x+8)<=0 then y=-2(-5x-8)+4 which is a linear equation.
Similarly
If (5x+8)>=0 then y=-2(5x+8)+4 which is also a linear equation

Any vertex must exist at the point where these two condition meet;
That is when (5x+8) = 0
at (x,y) =(-8/5,4)

The y-intercept occurs when x=0
y = -2abs(5(0)+8)+4 = -12

The x-intercepts occur when y=0
Case 1: (5x+8)>= 0
0 = -2(5x+8)+4
5x+8 = 2
x= -6/5

Case 2: (5x+8)<0
0 = -2(-5x-8)+4 (-5x-8) = 2 -5x = 10 x = -2#

In summary

the critical point is at (-8/5,4)
the y-intercept is at (-12)
the x-intercepts are at (-6/5) and
graph{-2*abs(5x+8)+4 [-5.696, 4.17, -0.437, 4.493]}