# How do you find the vertex???

• Sep 26th 2009, 04:09 PM
mackenzie25
How do you find the vertex???
I'm working on graphing absolute value equations, and for one of my problems, I need to identify the vertex using two seperate system of equations; one for the x-coordinate, and one for the y-coordinate. I don't really understand how to do it, and my first attempt gave me the wrong answer. Does anyone understand how to do this? Any help would be appreciated.

Equation #1: y=-|x-2|-12

My work:
x-coordinate ...............y-coordinate
x=-|(0)-2| ..................y=-|x-2|-12
x=-|-2| .......................y=-|(-2)-2|-12
x=-(2) ........................y=-|-4|-12
x=-2 ...........................y=-4-12
...................................y=-16

I know that the y-coordinate is wrong, but I dont understand how to do the problem.

Equation #2: y=|2x+4|+3

My work:
x-coordinate .......................y-coordinate
x=|2(0)+4| .........................y=|2x+4|+3
x=|0+4| ............................y=|2(4)+4|+3
x=|4| ................................y=|8+4|+3
x=4 ...................................y=|12|+3
..........................................y=15

My apologies for all of the periods, I couldn't get it to space right.
• Sep 26th 2009, 10:52 PM
Hello mackenzie25
Quote:

Originally Posted by mackenzie25
I'm working on graphing absolute value equations, and for one of my problems, I need to identify the vertex using two seperate system of equations; one for the x-coordinate, and one for the y-coordinate. I don't really understand how to do it, and my first attempt gave me the wrong answer. Does anyone understand how to do this? Any help would be appreciated.

Equation #1: y=-|x-2|-12

My work:
x-coordinate ...............y-coordinate
x=-|(0)-2| ..................y=-|x-2|-12
x=-|-2| .......................y=-|(-2)-2|-12
x=-(2) ........................y=-|-4|-12
x=-2 ...........................y=-4-12
...................................y=-16

I know that the y-coordinate is wrong, but I dont understand how to do the problem.

Equation #2: y=|2x+4|+3

My work:
x-coordinate .......................y-coordinate
x=|2(0)+4| .........................y=|2x+4|+3
x=|0+4| ............................y=|2(4)+4|+3
x=|4| ................................y=|8+4|+3
x=4 ...................................y=|12|+3
..........................................y=15

My apologies for all of the periods, I couldn't get it to space right.

The vertex will occur where the expression inside the absolute value symbols, \$\displaystyle |...|\$, has the value zero. From this, you can work out the value of \$\displaystyle x\$, and hence the value of \$\displaystyle y\$.

So for equation #1:

\$\displaystyle |x-2|=0 \$

\$\displaystyle \Rightarrow x = 2\$

Plug this value of \$\displaystyle x\$ into the equation for \$\displaystyle y\$:

\$\displaystyle y = -|2-2| -12\$

\$\displaystyle \Rightarrow y =0 -12\$

\$\displaystyle \Rightarrow y = -12\$

So the vertex is at \$\displaystyle (2,-12)\$

And for #2:

\$\displaystyle |2x+4|=0\$

\$\displaystyle \Rightarrow 2x=-4\$

\$\displaystyle \Rightarrow x = -2\$

And so \$\displaystyle y = |2(-2)+4|+3\$

\$\displaystyle \Rightarrow y = |0| +3\$

\$\displaystyle \Rightarrow y = 3\$

So the vertex is at \$\displaystyle (-2,3)\$