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)?

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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