ADVANCED EXERCISES

(1)

 Find the equations for the parabolas described below:

 (a) vertex is 2 units from the x-axis, opens downward, symmetric about x = 1, 
     y-intercept = 23/12

 (b) has vertical axis of symmetry and passing through (-2,3), (0,3), and 
     (1,9).

 (c) Opens upward, passing through (-2,7), vertex is on the positive 
     y-axis and is 5 units from the origin.

 (d) Find an equation that represents a parabola which opens to the 
     right, has its vertex at (2,2) and passes through the point (5,0).

HINT:

The trick to these problems is to solve for the constant, C, and the 
coefficients, A and B.  A good approach is to solve for C first, then create 
a system of equations that will allow you to solve A and B.

(a) Remember Standard Form y = Ax2 + Bx + C.  Use point (0, 23/12) to solve C.  
(h, k) = (-B/2A , C- (B2/4A))