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that1chick

  • 2 years ago

Rewrite y = 3x2 - 24x + 10 in general form.

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  1. Mertsj
    • 2 years ago
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    General Form You have already seen how to graph a quadratic function when it is in its standard form. Recall that the standard form of a quadratic function looks like: y=a(x-h)^2+k But how do you graph a quadratic function when it is in its general form? The general form of a quadratic function looks like this: y=ax^2+bx+c

  2. Mertsj
    • 2 years ago
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    So how does your author define general form?

  3. that1chick
    • 2 years ago
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    h=x, k=y... the problem I'm having with this one is splitting the 3 in 3x^2...?

  4. that1chick
    • 2 years ago
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    Its just asking to rewrite it not graph it... heres what I have so far:

  5. Mertsj
    • 2 years ago
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    So you want h-k form?

  6. that1chick
    • 2 years ago
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    -10 on both sides Y-10=3x^2-24x 24/2=12 12^2=144 Y-10=3x^2-24x+144

  7. that1chick
    • 2 years ago
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    Its in standard form, I want general form(:

  8. Mertsj
    • 2 years ago
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    Let's write it like this: |dw:1362857059987:dw|

  9. Mertsj
    • 2 years ago
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    Now complete the square inside the parentheses

  10. that1chick
    • 2 years ago
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    OH! gcf! of course!!:D

  11. Mertsj
    • 2 years ago
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    |dw:1362857161791:dw|

  12. that1chick
    • 2 years ago
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    Thank you(: I forgot to look for a gcf

  13. Mertsj
    • 2 years ago
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    yw

  14. that1chick
    • 2 years ago
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    Y-10=3x^2-24x+144 Now factor the GCF y-10=3(x^2-8x+48) y-10=3(x-4)(x+12) +10 to both sides Y=3(x-4)(x+12) +10 Right?

  15. that1chick
    • 2 years ago
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    how did you get 16^^

  16. that1chick
    • 2 years ago
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    Oh wait... I know

  17. Mertsj
    • 2 years ago
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    No. You cannot add 48 to one side without adding it to the other side. Did you see in my example that I added 16 inside the parentheses to complete the square? But I was really adding 48 to the right side because there is a 3 outside the parentheses. So then I subtracted 48 so there would be a net change of 0. Of course I could have added 48 to the left side which would have accomplished the same purpose.

  18. Mertsj
    • 2 years ago
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    16 is the number that completes the square for x^2+8x

  19. that1chick
    • 2 years ago
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    1 sec..

  20. that1chick
    • 2 years ago
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    Y-10=3x^2-24x GCF Y-10=3(x^2-8x) Complete the square 8/2=4 4^2=16 y-10=3(x^2-8x-16) Simplify y-10=3(x-4)^2 +10 to both sides y=3(x-4)^2 +10 Right?

  21. that1chick
    • 2 years ago
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    and by simplify I mean find the binomial...(:

  22. Mertsj
    • 2 years ago
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    So let's multiply out your result: \[y=3(x-4)^2+10=3(x^2-8x+16)+10=3x^2-24x+48+10=\]

  23. Mertsj
    • 2 years ago
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    \[3x^2-24x+58\]

  24. Mertsj
    • 2 years ago
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    Is that the problem you started with?

  25. Mertsj
    • 2 years ago
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    If it isn't, then what you have done is changed the original problem instead of keeping the original problem and expressing it in another form.

  26. that1chick
    • 2 years ago
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    What am I doing wrong?

  27. Mertsj
    • 2 years ago
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    When you add 48 to the right side, you then have 2 choices: 1. subtract 48 from the right side 2. Add 48 to the left side.

  28. that1chick
    • 2 years ago
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    y-10=3x^2-24x y-10=3x^2-24x+48 +48 y+38=3x^2-24x+48

  29. that1chick
    • 2 years ago
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    y+38=3(x^2-8x+16) y+38=3(x-4)^2 Right so far?

  30. that1chick
    • 2 years ago
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    Ok I solved it out on paper(: thank you for helping me

  31. Mertsj
    • 2 years ago
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    yes

  32. Mertsj
    • 2 years ago
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    yw

  33. that1chick
    • 2 years ago
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    24/2=12 12^2=144........

  34. Mertsj
    • 2 years ago
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    That is true. Not sure it is very useful.

  35. that1chick
    • 2 years ago
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    y-10=3x^2-24x+144

  36. that1chick
    • 2 years ago
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    k, never mind

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