Question

The equation of a parabola is given.

Answer 1

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