SOLUTION: Arrange the problem is represented by the equations in increasing order with respect to the Y values of the directrixes. y=-x^2+3x+8 y=2x^2+15x+18 y=x^2+13x+5 y=-2x^2+4x+8

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Arrange the problem is represented by the equations in increasing order with respect to the Y values of the directrixes. y=-x^2+3x+8 y=2x^2+15x+18 y=x^2+13x+5 y=-2x^2+4x+8      Log On


   

Question 1085007: Arrange the problem is represented by the equations in increasing order with respect to the Y values of the directrixes.
y=-x^2+3x+8
y=2x^2+15x+18
y=x^2+13x+5
y=-2x^2+4x+8
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
y=ax%5E2%2Bbx%2Bc

ax%5E2%2Bbx%2Bc=y

ax%5E2%2Bbx=y-c

x%5E2%2Bexpr%28b%2Fa%29x=expr%281%2Fa%29y-c%2Fa

Complete the square on the left:

       expr%28b%2Fa%29%2Aexpr%281%2F2%29=b%2F%282a%29
       %28b%2F%282a%29%29%5E2=b%5E2%2F%284a%5E2%29



%28x%2Bb%2F%282a%29%29%5E2=%281%2Fa%29%28y-%284ac-b%5E2%29%2F%284a%5E%22%22%29%29

Compare to

%28x-h%29%5E2=4p%28y-k%29

h=-b%2F%282a%29, k=%284ac-b%5E2%29%2F%284a%5E%22%22%29, 4p=1%2Fa, p=1%2F%284a%29

The equation of the directrix is 



y+=+%284ac-b%5E2%2B1%29%2F%284a%5E%22%22%29 <-- equation of directrix

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y=-x^2+3x+8, substitute in above, a=1, b=3, c=8, directrix: y = 6 

y=2x^2+15x+18, substitute a=2, b=15, c=18, directrix: y = -10 

y=x^2+13x+5, substitute a=2, b=13, c=5, directrix: y = -37 

y=-2x^2+4x+8, substitute a=-2, b=4, c=8, directrix: y = 9.975

Edwin