Question 206447
There are several forms in which the equation of a parabola can be written.  One of them is vertex form, because the vertex can be read directly off of it. the form is:
{{{ y = a(x-h)^2 + k }}} where (h,k) is the vertex, occasionally written as {{{ y - k = a(x-h)^2 }}}.  If the parabola opens up then a is a positive number, and if the parabola opens down then a is a negative number.
 
If the parabola opens right (a+) or left a-), then the equation would be {{{ x = a(y-k)^2 +h }}} where (h,k) is the vertex,  or  {{{x - h = (y - k)^2 }}}. (note the y part is squared and the x part is not)
 
In the case of yours, then you have {{{ y = a(x-0)^2 + 2 }}} and a is negative.  So, how do you find a?  Well, you talk about an equation having points.  That means if you plug the x and the y coordinates of the point into x and y, respectively, the equation you should come out with a true statement/equation.  So, let's take one of the other points (the vertex won't help you find a (Why?) ), how about (2,-2) ... when you plug 2 in for x and -2 in for y, you have:
{{{ -2 = a(2-0)^2 + 2 }}}
{{{ -4 = 4a + 2 }}}
{{{ a=-1}}}

So an equation for your parabola is {{{ y = -1(x-0)^2 + 2 }}}  --  of course the  1 in the -1  and the -0 in the x-0 could be dropped: {{{ y = -x^2 + 2 }}}.
 
The graph looks like:
{{{ graph(300,300,-3,3,-3,3,-x^2 + 2) }}}
 
Other forms of the equation are {{{ y = ax^2 + bx + c }}} and {{{ y = a(x-b)(x-c) }}}
 
  -  Mick