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anonymous

  • 5 years ago

Find the vertex and all intercepts of the quadratic function f(x) = –2x2 + 12x – 15.I need to review for a test, plz help

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  1. anonymous
    • 5 years ago
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    hello

  2. amistre64
    • 5 years ago
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    hi

  3. amistre64
    • 5 years ago
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    the vertex x compnent is -12/-4 = 3; use that value to determine the y component teh rest is either complete the square, or quadrtic formula it... you get the same results

  4. anonymous
    • 5 years ago
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    where you get -12/-4=3?

  5. anonymous
    • 5 years ago
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    you their?

  6. amistre64
    • 5 years ago
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    ok.... lets do it this way; we want the first# to be 1; so divide it all by -2: y = x^2 -6x +15/2 = 0 for simplicities sake x^2 -6x + ___ = -15/2 ; we subtracted 15/2; now we wanna complete the square on the left side we complete the square by making it a perfect square; so we need a number that when added to itself makes -6; then we can square that number to complete it :) x^2 -6x + ___ = -15/2 -3 + -3 = -6; -3(-3) = 9, lets use 9 to fill in the blank x^2 -6x +9 = -15/2 +9 ; we added 9 to each side, now convert the left side to its perfect square look, and add the rightside together like this: (x-3)^2 = 3/2 ; now sqrt both sides x-3 = +- sqrt(3/2) ; now add 3 to both sides to get x = 3 +- sqrt(3/2) ; and dbl chech to make sure I didnt mess it up lol

  7. anonymous
    • 5 years ago
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    you did the whole problem their?

  8. anonymous
    • 5 years ago
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    you did the whole problem their?

  9. anonymous
    • 5 years ago
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    you did the whole problem their?

  10. amistre64
    • 5 years ago
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    the first number there is the vertexes 'x' component; use it to find the 'y' component. the roots are simply what x =: x = 3 + sqrt(3/2) AND x = 3 - sqrt(3/2)

  11. amistre64
    • 5 years ago
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    another way would be to solve it for the geometric interpretation of the equation; which is similar except we dont use =0, we use =y y = –2x2 + 12x – 15 (-1/2)y = x^2 -6x +15/2 (-1/2)y -15/2 = x^2 -6x -16y/2 +9 = x^2 -6x +9 -4y +9 = (x-3)^2 -4(y - 9/4) = (x-3)^2 vertex = (3, 9/4)

  12. amistre64
    • 5 years ago
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    that looks odd lol

  13. amistre64
    • 5 years ago
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    16/2 = 8 lol i forgot how to divide by 2 :)

  14. amistre64
    • 5 years ago
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    -8y +9 = (x-3)^2 -8 (y - 9/8) = (x-3)^2; vertex = (3, 9/8) ?? lets check: –2(3)^2 + 12(3) – 15 = y -18 -15 +36 = y -33 + 36 = y 3 = y .... well, I got the x right lol

  15. amistre64
    • 5 years ago
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    my mistake was thinking I could combine -y/2 and -15/2 .... silly me

  16. amistre64
    • 5 years ago
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    (-1/2)y -15/2 +9 = x^2 -6x +9 (-1/2)y +3/2 = (x-3)^2 (-1/2) (y-3) = (x-3)^2 vertex = (3,3) that did it ...

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