Difference between standard forms of parabolas

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Nikolas111

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Apr 4, 2016
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Hello, Good evening for everybody
I would like to plead you to explain me why in my country is standard form for parabolas (x-h)^2=+-2p(y-k) and for english Maths it is (x-h)^2= +-4p(y-k) and which one is correct and why:)
Thank you very much in advance .
 
What is the Definition of "p"? This will help you find the right one. Vertex Form?

As far as "Standard Form", that rare gives useful information. It's a good starting place. For a parabola, usually y = ax^2 + bx + c

As far as names of things. "Standard" isn't always that standard. There can be variation among authors and countries and attitudes.
 
Well, I can't speak for why your or my country does anything but what is or is not "standard" form is pretty much "convention" so I would not call either of those "correct". In fact, I am used to the "standard form" for a parabola being not either of those but \(\displaystyle y= ax^2+ bx+ c\). The two forms you give are what I would call "vertex form". In the vertex form \(\displaystyle (x-h)^2= +-4p(y-k)\) (h, k) is the vertex. p is the distance from the vertex to the focus of the parabola. In the other form, \(\displaystyle (x-h)^2= +-2(y-k)\) "p" is twice the distance from the vertex to the focus.
 
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