SOLUTION: 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)

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
---
Using (-2,-2) and (2,-2) you get
-2 = 4a +2
a = -1
================
Equation:
y = -x^2+2
=================
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.
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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)
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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: .
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The graph looks like:

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Other forms of the equation are and
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- Mick
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