How do you find the intercepts and vertex for # y=-2|5x+8|+4#?

1 Answer
SCooke
Sep 23, 2017

Intercepts: # x = -6/5# ; and #x = 6/5#
Vertex: (0, -12)

Explanation:

At x = 0, y = -12. The absolute value function just means that the graph will be symmetric about some point, forming a “V” shape in the case of a linear equation. The x intercepts are:
#−2|5x+8|+4 = 0# ; #−2|5x+8| = -4# ; #|5x+8| = 2# ; #+(5x+8) = 2# and #-(5x+8) = 2# ;
# 5x = -6# ; # x = -6/5# and #-5x = -6#; #x = 6/5#
The vertex must be the point midway between these two for the linear symmetry. That will be the point at x = 0, where we have already found y to be -12.

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