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I am indeed making my return to answer questions on this site once i finish my math final, in the meantime, i have a few problems to finish for my homework XD

 

What is the vertex of the graph of \(f(x)=a|bx-1|+c\)?

I am confused as to how I reach it since it has no real numbers and I cannot graph it...

How do I reach it?

 Jun 21, 2018
 #1
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The  x  coordinate of the vertex is the  x  value that makes whatever is in the absolute value be  0  .

 

So to find the  x  coordinate of the vertex, set what is inside the absolute value equal to  0 .

 

bx - 1  =  0      Now let's solve this equation for  x .

bx  =  1

x  =  1/b

 

To find the  y  coordinate of the vertex, plug in the  x  coordinate of the vertex into the function.

 

f( 1/b )  =  a | b(1/b) - 1 | + c

f( 1/b )  =  a | 0 | + c

f( 1/b )  =  c

 

So the vertex is  (1/b, c)

 

Take a look at this graph and try moving the sliders to help see it:

https://www.desmos.com/calculator/tcxtdfrpod   

 Jun 21, 2018

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