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?

OfficialBubbleTanks
Jun 21, 2018

#1**+1 **

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:

hectictar
Jun 21, 2018