# Vertex of Absolute Value Equations

by FARAWAY
(PA)

CALCULATING THE VERTEX OF AN ABSOLUTE VALUE OF THE EQUATION

WRITE DOWN WHAT IS INSIDE THE ABSOLUTE VALUE SYMBOL AND SET EQUAL TO ZERO

SOLVE FOR "X"

SUBSTITUTE THE VALUE OF X INTO THE ORIGINAL EQUATION AND SOLVE FOR "Y"

WRITE THE ORDERED PAIR

Y=(X)-2

y=-10(X=4)-5

Y= -(X-5)

Y= (X)

THE LAST QUESTION COULD BE ANY NUMBER BUT THE SAME NUMBER THAT IS POSITIVE FOR BOTH X AND Y?
OR IT CAN BE ANY NEGATIVE NUMBER BUT THE SAME NUMBER THAT IS NEGATIVE ON BOTH SIDE BUT THE ANSWER FOR BOTH OF THESE WILL BE POSITIVE?

IS THAT CORRECT FOR Y=(X)?

Karin from Algebra Class Says:

Your explanation for finding the vertex of an absolute value equation is exactly correct!

Let's look at Example 1: y = |x| - 2
x = 0 x is inside the absolute value
symbol, so set it equal to 0.

y = |0| - 2 Substitute the value for x back
into the equation and solve for
y.
y = 0-2
y = -2

The vertex for y = |x| - 2 is (0, -2)

Example 2: y= -10|x+4| - 5

Step 1: Set x + 4 = 0 & Solve.
x + 4 = 0

x + 4 - 4 = 0 - 4
x = -4
Step 2: Substitute -4 for x back into the equation and solve for y.

y =-10|x+4| - 5
y =-10|-4+4| - 5
y =-10(0) -5
y = -5

The vertex for y= -10|x+4| - 5 is (-4, -5)

Example 3: y = -|x-5|

Step 1: set x - 5 = 0
x - 5 = 0
x- 5 + 5 = 0 + 5
x = 5

Step 2: Substitute 5 for x and solve for y.
y = -|x-5|
y = -|5-5|
y = -(0)
y = 0

The vertex for y = -|x-5| is (5,0)

It looks like you are on the right track!

Good luck,
Karin

### Comments for Vertex of Absolute Value Equations

Average Rating     Nov 19, 2019 Rating     Clear & to the point! by: Kofi Yankey Very well explained and demonstrated. I also agree to point out that a "-" outside the absolute value sign means it doesn't hold water or is upside down. And a positive absolute value would show that it does "hold water" or V-shaped upwards.Excellent!!!

 Apr 17, 2018 Rating     LEL by: Billy Thx m8. 1 needed th!s b@d1y

 Sep 25, 2017 Rating     Good job by: Vobo Caleb Wow! It works like magic. Thanks

 Mar 05, 2013 Rating     Good by: Anonymous Very nicely elucidated on. One suggestion: In the last problem for instance, Y =-⎮X-5⎮ it might be a good idea to state that the graph points downwards, i.e., that it will not hold water. Otherwise, you did a beautiful Job Sincerely, Harry Dunleavy

 Dec 04, 2012 Rating     thanks soo much by: An 8th grade elgabra student this REALY helped i was sick for 3days of school and my teacher wouldnt catch me up so i had to do it on my own and this helped me ace 2 of my worksheets!!! thanks alot

 Feb 07, 2012 Rating     :) by: Maria thanks x 1000! :D

 Mar 02, 2011 Rating     nice by: Anonymous thumbs up nice work job done Need More Help With Your Algebra Studies?