Question 1170537
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Given: the directrix is the line y=-3; the focus is at (2,0).<br>
With that information, we know the parabola opens upward.<br>
The distance from the directrix to the focus is 3 (from y=-3 to y=0).<br>
The vertex is halfway between the directrix and the focus -- at (2,-1.5).<br>
The vertex form of the equation is<br>
{{{y = ((1/(4p))(x-h)^2)+k}}}<br>
where (h,k) is the vertex and p is the directed distance from the directrix to the vertex, or from the vertex to the focus.<br>
The given information leads us to a vertex at (2,-1.5) and a p value of 1.5.  So the equation is<br>
{{{y = ((1/6)(x-2)^2)-1.5}}}<br>