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anonymous

  • one year ago

What are the coordinates of the vertex for f(x) = 2x2 + 4x + 9? (−2, 4) (−1, 7) (1, 15) (2, 9)

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  1. Nnesha
    • one year ago
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    formula to find x coordinate of vertex \[\huge\rm x=\frac{ -b }{ 2a }\]

  2. Nnesha
    • one year ago
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    then substitute all x in f(x) equation for its value to find y-coordinate of vertex

  3. anonymous
    • one year ago
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    what do i put for the a and b?

  4. Nnesha
    • one year ago
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    a=leading coefficient b=middle term \[\huge\rm \color{reD}{A}x^2+\color{blue}{B}x+C=0\]

  5. anonymous
    • one year ago
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    ok thank you

  6. anonymous
    • one year ago
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    do i leave the negative sign in front of the b even when it's a positive?

  7. Nnesha
    • one year ago
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    yes b is positive but negative is in the formula so that stays there

  8. anonymous
    • one year ago
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    so it would be \[x=\frac{ -4 }{ 2(2)}\]?

  9. Nnesha
    • one year ago
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    yep right

  10. anonymous
    • one year ago
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    so -4/4 and i would just divide it and it would come out as -1 right?

  11. Nnesha
    • one year ago
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    yes that's x-coordinate

  12. anonymous
    • one year ago
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    how do i find the y-coordinate now?

  13. Nnesha
    • one year ago
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    now to find y -coordinate substitute x for -1 \[\rm \color{reD}{x=-1}\] \[\huge\rm 2\color{reD}{x}^2+4\color{red}{x}+9=0\]

  14. anonymous
    • one year ago
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    so the y-coordinate would be 3? (-1,3)?

  15. Nnesha
    • one year ago
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    mhm

  16. Nnesha
    • one year ago
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    when you take square of negative number you will get positive number

  17. anonymous
    • one year ago
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    how do i do that

  18. Nnesha
    • one year ago
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    \[\huge\rm 2\color{reD}{(-1)}^2+4\color{red}{(-1)}+9=0\] now solve (-1)^2 is same as -1 times -1 = ?

  19. anonymous
    • one year ago
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    so 1?

  20. Nnesha
    • one year ago
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    yes -1 times -1 = 1 (-1)^2=1 so solve \[\huge\rm 2\color{reD}{(1)}+4\color{red}{(-1)}+9=?\]

  21. anonymous
    • one year ago
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    oh so (-1,7)

  22. Nnesha
    • one year ago
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    yep

  23. anonymous
    • one year ago
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    could you help me out with another one

  24. anonymous
    • one year ago
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    @Nnesha

  25. Nnesha
    • one year ago
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    i'll try

  26. anonymous
    • one year ago
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    What is the equation of the quadratic graph with a focus of (5, −1) and a directrix of y = 1? f(x) = −one fourth (x − 5)2 + 1 f(x) = one fourth (x − 5)2 + 1 f(x) = −one fourth (x − 5)2 f(x) = one fourth (x − 5)2

  27. anonymous
    • one year ago
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    @Nnesha ?

  28. Nnesha
    • one year ago
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    well not sure about this need to review this stuff hmm

  29. Nnesha
    • one year ago
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    sorry

  30. anonymous
    • one year ago
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    its fine. i got it Cx thank you tho !

  31. Nnesha
    • one year ago
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    np

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