Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.

1: y = - x2 + 3x + 8

2: y = 2x2 + 15x + 18

3: y = - x2 + 7x + 14

4: y = - 2x2 + 9x + 7

5: y = x2 + 13x + 5

6: y = - x2 + 8x + 5

7: y = - 2x2 + 4x + 8

(x-h) ^2=4P (y-k), vertex is (h, k)

P is distance from vertex to directix

remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k

nut

ok so one way is to just graph them on a graphing utility

remember if the graph opens up, then the directix is below that

or we can convert to 4P (y-k) = (x-h) ^2 form where P is distance from directix

I will only convert the 1st one fully, you should be able to do the rest

1. y=-x^2+3x+8

multiply both sides by - 1 since we don't like the x^2 term negative

-y=x^2-3x-8

add8 to both sides

-y+8=x^2-3x

take 1/2 of linear coeficient and square it and add to both sides

-3/2=-1.5

(-1.5) ^2=2.25

-y+10.25=x^2-3x+2.25

factor perfect square

-y+10.25 = (x-1.5) ^2

force undistribute - 1 in left side

(-1) (y-10.25) = something, we don't care anymore for now

factor out a 4 in - 1

4 (-1/4) (y-10.25)

k=10.25

p=-1/4=-0.25

directix=k-p=10.25 - (-0.25) = 10.5

directix is y=10.5

basically completee the square with x and find P by force factoring a 4 out

2. directix: y=-1.75

3. directix: y=1.5

4. directix: y=17.25

5. d: - 37.5

6. d: 9.25

7. d=2.625

order them yourself