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27 October, 14:19

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

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  1. 27 October, 14:45
    0
    (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
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