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?
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: