SOLUTION: What is the vertex and focus of the parabola whose equation is {{{(y-8)^2 = -4(x-4)}}}?

You must memorize:

"U-parabolas"

Parabolas which open upward or downward have equation:



with vertex (,), focus (,),

the horizontal line which is the directrix has the
equation .

the vertical line which is the axis of symmetry has the
equation .
 
If p is positive the parabola opens upward. If p is
negative the parabola opens downward

-----

C-parabolas

Parabolas which open rightward or leftward have equation:



with vertex (,), focus (,),

the vertical line which is the directrix has the
equation .

the horizontal line which is the axis of symmetry has the
equation .

If p is positive the parabola opens rightward. If p is
negative the parabola opens leftward.

----



we compare this to

, so the parabola opens right or left

 so 

 so 

 so , a negative number, so the
parabola opens left

So the vertex is (,) = (4,8)

The focus is (, ) = (,) = (,) = (,)

the vertical line which is the directrix has the
equation , or  or  or 

the vertical line which is the axis of symmetry has the
equation , or .

To draw the parabola,  plot the focus, vertex, and directrix



Draw a line from the focus thru to vertex to the directrix.



Use that line as a side of a square, draw one square above:



and draw another square below:



Finally sketch in the parabola with the vertex (,)
passing through corners of those two squares.



Edwin