Question

Any help greatly appreciated!!! Will fan and medal!!

A manufacturer is designing a two-wheeled cart that can maneuver through tight spaces. On one test model, the wheel placement (center) and radius is modeled by the equation (x + 2)^2 + (y – 0.5)^2 = 16. What is the graph that shows the position and radius of the wheels?

Answer 1

@jim_thompson5910 Do you think you could help me figure this out??

Answer 2

@abb0t Do you think you could help me with this?

Answer 3

Still need help @Wimsicle ?

Answer 4

Yes please! (:

Answer 5

Aight. Lots of engineering text there but we need to graph (x + 2)^2 + (y – 0.5)^2 = 16
Right?

Answer 6

Right!

Answer 7

Alright. There is a bit of background knowledge needed here.
Suppose I have the graph of
y=x^2
When I modify one of the variables (any I chose) in some ways, the resulting graph can be predicted based on the graph of y=x^2. Are you familiar with this?

Answer 8

I think so

Answer 9

How could we apply that concept to this problem?

Answer 10

In the case where we "translate a variable": fancy wording for doing something like replacing x with x+2,
x -> 2
The graph is translated in the opposite direction i.e. it shifts by -2 along the x axis.
We can do more stuff to variables, but simple translation will work for this case.
For example, if I have the graph
y=x^2

Then I replace x with x-2, x -> x-2
My new equation becomes
y=(x-2)^2
And I can predict that the graph will move by 2 in the +x direction

Makes sense so far?