Question 1180070
Based on the equations of the parabolas, identify each parabola whose focus and vertex lie in different quadrants.

a. y=-x^2/8+x/4+23/8
b. y=x^2/32+x/4-13/2
c. x=-y^2/16-y/4+11/4
d. x=y^2/16+y/4-19/4
e. x=-y^2/36-5y/18+299/36
f. y=-x^2/24-5x/12+95/24
<pre>DEFINITELY not going to do all of those for you, JUST # 1.
If you like TORTURE, then you can do the problem the same way the other COMPLEX-PERSON who responded, did it! If you do not wish to TORTURE yourself, then read on.
{{{matrix(1,3, y, "=", (- x^2)/8 + x/4 + 23/8)}}}
{{{matrix(1,3, 8y, "=", - x^2 + 2x + 23)}}} ------- Multiplying by LCD, 8
{{{matrix(1,3, x^2 - 2x, "=", - 8y + 23)}}}
{{{matrix(1,3, x^2 - 2x + ((1/2) * - 2)^2, "=", - 8y + 23 + ((1/2) * - 2)^2)}}} ----- Complete the square on x by taking {{{1/2}}} of "b" on x, squaring it and ADDING it to both sides
{{{matrix(1,3, x^2 - 2x + (- 1)^2, "=", - 8y + 23 + (- 1)^2)}}} 
{{{matrix(2,3, (x - 1)^2, "=", - 8y + 23 + 1, (x - 1)^2, "=", - 8y + 24)}}}
Final equation, with a VERTICAL AXIS of SYMMETRY: {{{highlight_green(matrix(1,3, (x - 1)^2, "=", - 8(y - 3)))}}} 
                            Compare the above to: {{{matrix(1,3, (x - h)^2, "=", 4p(y - k))}}}, where: {{{matrix(4,3, Vertex, "is:", "(h, k)", Focus, "is:", "(h, k + p)", Directrix, "is:", y = k - p, Axis_of_Symmetry, "is:", x = h))}}}