Expert: Richard J. Raridon - 10/16/2004

Question
Hi, I need your help with a couple problems Im not understanding, this is what you have to do. Without drawing the graph of the given equations, determine how many y intercepts the parabola has an wheather its vortex lies above or below or on the x axis.

1. y= x squared - 5x + 6
2. y= -x squared + 2x -1

Answer
1. y = x^2 -5x +6
dy/dx = 2x -5 = 0 so x = 5/2 at the minimum or maximum.
Put that value into the equation and y = -1/4 so the vertex is below the axis.
2. y = -x^2 +2x -1
dy/dx = -2x +2 = 0 so x = 1
and at x=1, y = 0 so the vertex is on the axis