Respuesta :

To make this as easy as possible, we will find the vertex from the equation above.  The vertex is sitting at (h, k) of (2, -3).  The directrix is the same number of units from the vertex that the focus is.  The formula for the focus for an upwards-opening parabola is [tex](h,k+ \frac{1}{4a} ) [/tex].  The "a" in that formula is the 1/4 sitting in front of (y+3).  Filling in accordingly, we have [tex](2, -3+ \frac{1}{4( \frac{1}{4}) }) [/tex].  Simplifying we get [tex](2, -3+1)=(2, -2)[/tex].  The focus is on the axis of symmetry along with the vertex, and is 1 unit above the vertex. That means that the directrix is 1 unit BELOW the vertex and is a horizontal line.  Therefore, the directrix has an equation of y = -4
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