SOLUTION: A vertical parabola has a vertex at (-3,-2) and passes through the point (-1,7). Find the equation of the parabola, the equation of the directrix, and the coordinates of the focus

 

Hi,

the vertex form of a Parabola opening up(a>0) or down(a<0),  

where(h,k) is the vertex  and  x = h  is the Line of Symmetry

The standard form is , where  the focus is (h,k + p)

A vertical parabola has a vertex at (-3,-2) 

 y = a(x+3)^2-2    |passes through the point (-1,7). 

 7 = a(2^2)-2

 9/4 = a

 

    4p = 4/9,  p = 1/9   F(3, -17/9)