HYP20 Hyperbola requiring comple

HYP20 Hyperbola requiring completing the square

This is a hyperbola, and the presence of the linear terms indicates it is moved up and down and sideways. Graphing requires a completing the square approach. Follow the completing the square approach through the equations below. Watch the multiplication of the parentheses very carefully.

Make the identification X = x - 3 and Y = y + 4 so the function can be written

Draw in the new axes with origin at (3,-4). When X = 0, there are no real Y values.

When Y = 0,X = ±2. Place these points on the graph. The asymptotes come out of the y = … equation. Follow along the rearrangement to find the asymptote lines.

For large values of X, Y » ±(3/2)X. The addition of these asymptote lines allows completion of the graph. Again notice the box that helps in graphing the equation.