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

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Nov 19, 2019
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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
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LEL
by: Billy

Thx m8. 1 needed th!s b@d1y

Sep 25, 2017
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Good job
by: Vobo Caleb

Wow! It works like magic. Thanks

Mar 05, 2013
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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
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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
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:)
by: Maria

thanks x 1000! :D

Mar 02, 2011
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nice
by: Anonymous

thumbs up nice work job done

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