Question 118443
given:
{{{y= -(1/3)x^2+3x-1}}}

Find: Transformational Form  
{{{(1/a)(y - k) = (x - h)^2}}}


Since Standard Form is: 
{{{y = a(x-h)2+k}}}
Where ({{{h}}} and {{{k}}}) are vertex coordinates, we will find vertex first:



*[invoke completing_the_square "-(1/3)", 3, -1]


Transformational Form , 
{{{(1/a)(y - k) = (x - h)^2}}}

Since {{{a = -1/3}}}
{{{h =9/2 }}}}
{{{k = 23/4}}}

then
{{{1/(-1/3)(y - 23/4) = (x - 9/2)^2}}}

{{{(-3)(y - 23/4) = (x - 9/2)^2}}}