Question 1160185
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The vertex form of the equation of a parabola that opens up or down with vertex (h,k) is<br>
{{{y-k = (1/(4p))(x-h)^2}}}<br>
where p is the directed distance (that is, it might be negative) from the vertex to the focus.<br>
In this problem, all the information required to write the equation is given to you; there is no work to be done other than plug in the numbers.<br>
The vertex is (0,0); the directed distance from the vertex (0,0) to the focus (0,-3) is -3, so p = -3.<br>
Plug in the numbers:<br>
{{{y-(-3) = (1/(4(-3)))(x-0)^2}}}<br>
{{{y+3 = (-1/12)x^2}}}<br>
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Oops!  Tutor @MathTherapy spotted my error....  The vertex is (0,0), not (0,-3). So<br>
{{{y-0 = (1/(4(-3)))(x-0)^2}}}<br>
{{{y = (-1/12)x^2}}}<br>