The equation of a parabola is given. y = -5/8 x^2 - 3x + 4 what is the equation of the directrix of the parabola?

We have that
y = -5/8 x²- 3x + 4> multiply by 8> 8y=-5x²-24x+32
8y-32=-5x²-24x

Factor the leading coefficient

8y-32=-5*(x²+4.8x)

Complete the square  Remember to balance the equation by adding the same constants to each side.

8y-32=-5*(x²+4.8x+5.76-5.76)
8y-32-28.8=-5*(x²+4.8x+5.76)
8y-60.8=-5*(x+2.4)²
8*(y-7.6)=-5*(x+2.4)²
-(8/5)*(y-7.6)=(x+2.4)²
-(1.6)*(y-7.6)=(x+2.4)²

is a vertical parabola> open down
The standard form is (x - h)² = 4p (y - k)

the vertex is the point (-2.4,7.6)
4p=-1.6
p=-1.6/4> p=-0.40

the directrix is
 y= k - p> 7.6-(-0.40)> y=7.6+0.40> y=8

the answer is
y=8