Question

Find the vertices of the hyperbola with equation: ((x-1)^2/4) - ((y+2)^2/9) = 1?

Answer 1

the vertx cross along the x part; 2 away from center

Answer 2

c=(1,-2); verts are then (-1,-2) and (3,-2) if i see it right

Answer 3

Some great notes:
http://tutorial.math.lamar.edu/Classes/Alg/Hyperbolas.aspx
and
http://www.purplemath.com/modules/hyperbola.htm

Here are some awesome videos:
http://patrickjmt.com/conic-sections-hyperbolas-an-introduction/
and
http://patrickjmt.com/conic-sections-hyperbolas-an-introduction-graphing-example/

Hope this helps

Answer 4

Send (translate) all your x's to x+1 and your y's to y-2 so that you have your hyperbola centered on (0,0) gives x^2/4 -y^2/9 = 1 (standard position).

Then your vertices are +- root 4 on the x axis ie (2,0) and (-2,0).

Now send all your x's and y's back where they came from (-1 on the x's and +2 on the y's) to give (1,2) and (-3,2).