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Pre-Calc

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for the conic y=5x^2-40x+78 find an equation in standard form and its vertex, focus, and directrix

  • Pre-Calc -

    complete the square
    y = 5(x^2 - 8x + ....) + 78
    = 5(x^2 - 8x + 16 - 16) + 78
    = 5( (x-4)^2 - 16) + 78
    = 5(x-4)^2 - 80 + 78
    = 5(x-4)^2 - 2

    take over ....

  • Pre-Calc -

    What's my next step??

  • Pre-Calc -

    We could write our answer in the form
    y+2 = 5(x-4)^2

    take a look at
    http://jwilson.coe.uga.edu/emt725/class/sarfaty/emt669/instructionalunit/parabolas/parabolas.html
    half-way down the page at example 3
    and follow the steps.

  • Pre-Calc -

    thank you!

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