Question 1187357
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You are given the vertex (5,4); and given the focus (5,2), you know the parabola opens downward.<br>
The vertex form of the equation I prefer to use is<br>
{{{y-k = (1/(4p))(x-h)^2}}}<br>
where (h,k) is the vertex and p is the directed distance (i.e., can be negative) from the vertex to the focus.<br>
You are given (h,k) = (5,4); and the given vertex and focus tell us p = -2.  So 4p = -8, and the equation is<br>
{{{y-4 = -(1/8)(x-5)^2}}}<br>