Equations of parabolas?

Question

Write the equations of the parabolas with the following conditions:

a) with vertex (5,-3) and passing through (3,9)

b) passing through the points (-1,-6), (3,-12), and (2,-4.5)

Answer 1

(3,9) is above the vertex (5,-3), which fits an up-opening parabola. The general equation for an up-opening parabola is

y-k = a(x-h)², a>0

Plug in (3,9) and (5,-3):

9+3 = a(3-5)²

12 = a4

a = 3

Equation of the parabola:

y+3 = 3(x-5)²

http://www.flickr.com/photos/dwread/2816...

Note that there is another solution: (3,9) is to the left of vertex (5,-3), which fits a left-opening parabola. The general equation for a left-opening parabola is

x-h = a(y-k)², a<0

Plugging in (3,9) and (5,-3):

3-5 = a(9+3)²

-2 = 144a

a = -1/72

Equation of the parabola:

x-5 = (-1/72)(y+3)²

http://www.flickr.com/photos/dwread/2816...