Question 1170536
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Vertex form of the equation is<br>
{{{y = ((1/(4p))(x-h)^2)+k}}}<br>
where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.<br>
With the equation in this form, |4p| is also the length of the latus rectum.<br>
With the parabola opening downward, p is negative, so 4p = -8.<br>
Then you have all the parts you need to write the equation in vertex form:<br>
{{{y = ((-1/8)(x-1)^2)+2}}}<br>
Convert that to any desired form.<br>