Question 671743: Suppose a parabola has vertex (5, –3) and also passes through the point (6, 1). Write the equation of the parabola in vertex form.
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
The parabola can open either up, down, left or right. The problem is, the parabola that opens left or right is not a function as it fails the Vertical Line Test.
The two vertex-forms of a parabola are:
 : If  , parabola opens up. If  , parabola opens down.
 : If , parabola opens right. If , parabola opens left.
Sometimes, a substitutes for  .
So, either equations work. The only differences are: one is a function and one is not. One opens down and other opens left.
The first formula is more precise, as you can find the coordinates of the focus and the equation of the directrix.
if vertex ( , ) and also passes through the point ( , ), then we have
 ............., parabola opens up
if , then 
so, we have:
 ....your equation
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