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i am getting that it opens right, (correct.) but the vertex is not the same that i get...
\[\Large y^2 = 6x+14 \] right? Idk cos there's a positive sign in front of 6x which seems odd, like maybe a term is missing. Otherwise you can write it as (by factoring out a 6 on the right) \[\Large y^2 = 6(x+\frac{ 14 }{ 6})\] Which gives a vertex \[\large \left( -\frac{ 14 }{ 6 }, 0 \right)\]
to the right y^2=- opens to the left x^2=+ opens up x^2=- opens down
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