(x + 3)² = –20(y – 1)
Say you have the above equation of parabola.
x² + 6x + 9 = -20y + 20
x² + 6x + 9 - 20 = -20y
x² + 6x - 11 = -20y
dividing the whole equation by -20
(x² + 6x - 11)/-20 = y
-x²/20 - 6x/20 + 11/20 = y
Remember that slope is just the change in 'y' over the change in 'x'
For you to get the slope, you just have to differentiate.
y = -x²/20 - 6x/20 + 11/20
dy/dx = -2x/20 - 6/20
dy/dx = -x/10 - 3/10
Say you are to find the slope in a point where x=-3, then you'll just have to substitute x=-3 to dy/dx = -x/10 - 3/10
then you'll have the slope as
dy/dx = -(-3)/10 - 3/10
dy/dx = 3/10 - 3/10
dy/dx = 0 -----this correct since i've used the x value of the vertex of the parabola.