Question

1/4(y+3)=(x-2)^2 what is the directirx

Answer 1

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 $(h,k+ \frac{1}{4a} )$.  The "a" in that formula is the 1/4 sitting in front of (y+3).  Filling in accordingly, we have $(2, -3+ \frac{1}{4( \frac{1}{4}) })$.  Simplifying we get $(2, -3+1)=(2, -2)$.  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