Question 206447: what is the equation of a parabola graph?
The parabola opens downward. The vertex is (0,2). It also has points (-2,-2) and (2,-2)
Found 2 solutions by stanbon, mickclns:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! what is the equation of a parabola graph?
The parabola opens downward. The vertex is (0,2). It also has points (-2,-2) and (2,-2)
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Form: y = a(x-h)^2+k
Vertex: h = 0, k = 2
Ao,y = ax^2 +2
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Using (-2,-2) and (2,-2) you get
-2 = 4a +2
a = -1
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Equation:
y = -x^2+2
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Cheers,
Stan H.
Answer by mickclns(59) (Show Source):
You can put this solution on YOUR website! 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:
 where (h,k) is the vertex, occasionally written as  . 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  where (h,k) is the vertex, or  . (note the y part is squared and the x part is not)
In the case of yours, then you have  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:
So an equation for your parabola is  -- of course the 1 in the -1 and the -0 in the x-0 could be dropped:  .
The graph looks like:
Other forms of the equation are  and 
- Mick
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