Can someone help me learn Graphing a Parabola with a Vertex at the Origin?

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Can someone help me learn Graphing a Parabola with a Vertex at the Origin?

Mathematics
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My online class isn't explaining it well and I can't find videos with the problems I'm faced with.
These are one of the examples
Phantom Lord got this.

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first, covert it into either \(Ax^2 + bx + c = 0 \) or \(f(x) = y = a(x-h)^2 +k \) where \(h, k \) is your vertex and \(a\neq 0\) the first option is easier, the second option requires you to know how to complete the square
you can solve the vertex in the first one by using \(\large (x=\frac{-b}{2a},y = f(x)) \)
@nincompoop how would you put y=1/12x^2 in that first formula???
so if you have a standard form of \(y = 2x^2 - 4x + 3\) your vertex can be solved by identifying your coefficients a = 2 b = 4 c = 3 vertex \(\large \frac{-b}{2a} = \frac{-(2)}{2(4)} = -\frac{1}{4}\) then plug \(- \frac{1}{4} \) into all of the x in \(y = 2x^2+4x+3 \)
@nincompoop i think i'll just keep trying with youtube because you're confusing me even more
analyze the standard form \(y = Ax^2 + Bx +c \) you have three terms first term \(Ax^2 \) second term \(Bx \) third term \(c \)
ask yourself if the given equation has second or third term? if they don't show up it means it is zero anything +0 will remain the same
http://www.mathsisfun.com/geometry/parabola.html
http://mathbitsnotebook.com/Algebra1/Quadratics/QDVertexForm.html

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