Hello, I'm having what I assume is a simple problem of misunderstanding something basic. I want to figure out the x-intercepts of the equation y=2|x-3|+1. I know what the graph looks like. I know it doesn't have any x-intercepts. But when I try calculate the x-intercepts, I'm getting answers that tell me it should have x-intercepts and I don't know what I'm doing wrong.
My process:
y=2|x-3|+1
Substitute 0 for y.
0=2|x-3|+1
-(1/2)=|x-3|
-(1/2)=x-3 OR -(-(1/2)=x-3
5/2=x OR 7/2=x
The math I see says I should have x-ints at (5/2, 0) and (7/2, 0). But that can't be right because the V of the graph is shifted up by 1 unit relative to the x axis.
I thank you kindly for helping me understand this paradox.
My process:
y=2|x-3|+1
Substitute 0 for y.
0=2|x-3|+1
-(1/2)=|x-3|
-(1/2)=x-3 OR -(-(1/2)=x-3
5/2=x OR 7/2=x
The math I see says I should have x-ints at (5/2, 0) and (7/2, 0). But that can't be right because the V of the graph is shifted up by 1 unit relative to the x axis.
I thank you kindly for helping me understand this paradox.