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Barrelracing

  • one year ago

What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6? a) -1/6x^2 +4/3x + 11/6 b) 1/6x^2 - 4/3x - 11/6 c) 3/50x^2 + 11/25x + 3/5 d) 2/50x^2 + 11/25 + 2/5

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  1. freckles
    • one year ago
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    |dw:1444325601632:dw| the vertex is halfway between the directrix and the focus

  2. freckles
    • one year ago
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    what number is midway between -3 and -6?

  3. Barrelracing
    • one year ago
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    -4 and -5

  4. freckles
    • one year ago
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    but what number is midway between -3 and -6? hence do you know how to find the average of -3 and -6?

  5. Barrelracing
    • one year ago
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    oh no i dont

  6. freckles
    • one year ago
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    the average of two numbers is the sum of the numbers divided by 2

  7. Barrelracing
    • one year ago
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    i got -1.5

  8. freckles
    • one year ago
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    -3+(-6)=-9 -9/2 equals -4.5 not -1.5

  9. Barrelracing
    • one year ago
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    oh i did wrong sorry

  10. freckles
    • one year ago
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    -4.5 makes since because this number is halfway between -4 and -5

  11. freckles
    • one year ago
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    sense*

  12. freckles
    • one year ago
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    it is also the number halfway between -3 and -6

  13. freckles
    • one year ago
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    |dw:1444325972949:dw|

  14. freckles
    • one year ago
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    so our parabola looks like this roughly : |dw:1444326013448:dw|

  15. freckles
    • one year ago
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    anyways the equation is \[4p(y-k)=(x-h)^2 \\ \text{ where } (h,k) \text{ is the vertex } \\ \text{ and } p \text{ is the distance between the vertex and the focus } \\ \text{ we also have } p>0 \text{ here since the vertex is above the directrix } \\ \text{ if it was the other way around we would have } p<0\]

  16. Barrelracing
    • one year ago
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    ok thank you i get it now

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