what are the coordinates of the focus of the parabola? (X+1)^2=-8(y-2)A. (-1,1)B. (-1,2)C. (-1,0)D. (1,-2)

Answer:C. (-1, 0)Step-by-step explanation:(You don't need a picture to figure this out...it's simple algebraic manipulation.)We could start off by rewriting the equation for the parabola with the negative on the other side, which tells us then that the parabola opens downward:[tex]-(x+1)^2=8(y-2)[/tex]Dividing both sides by -1 doesn't change anything.  Because this parabola opens downward, the focus is p units below the vertex at the same x-coordinate.  The vertex can be found from the equation to be (-1, 2).  The standard form of a parabola of this type is[tex]-(x-h)^2=4p(y-k)[/tex]where is the number of units between the vertex and the focus.  Our equation to find p is:4p = 8 so p = 2.That means that the focus is 2 units below the vertex at the x coordinate of -1.  Moving 2 units down from the y coordinate of 2 leaves us at a y coordinate of 0.  Therefore, the coordinates of the focus have to be (-1, 0)