How do you solve the absolute value equation y=−2|5x+8|+4 and find the vertex, x intercepts and y intercept?

1 Answer
Alan P.
May 28, 2015

Given y=−2|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)=(−85,4)

The y-intercept occurs when x=0
y=−2|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=−65

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

In summary

the critical point is at (−85,4)
the y-intercept is at (−12)
the x-intercepts are at (−65) and
graph{-2*abs(5x+8)+4 [-5.696, 4.17, -0.437, 4.493]}

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