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anonymous

  • one year ago

Using the completing-the-square method, rewrite f(x) = x2 + 4x − 1 in vertex form

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  1. anonymous
    • one year ago
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    Group the terms like this \[f(x)=(x^2+4x)-1\] Take the coefficient of x, divide it by 2 and square it. What's \(\left( \frac{ 4 }{ 2 } \right)^2\) ?

  2. anonymous
    • one year ago
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    4

  3. anonymous
    • one year ago
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    Right, so add 4 inside the parentheses. This means you also have to subtract 4 outside, so the equation doesn't change. \[f(x)=(x^2+4x+4)-1-4\]

  4. anonymous
    • one year ago
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    Now factor the part in parentheses, and combine like terms on the outside

  5. anonymous
    • one year ago
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    so would it be f(x)=(x^2+4x+4)-5

  6. anonymous
    • one year ago
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    yes, but you also have to factor x² + 4x + 4

  7. anonymous
    • one year ago
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    oh I got it. But can you help me with a few others?

  8. anonymous
    • one year ago
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    ok

  9. anonymous
    • one year ago
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    Using the completing-the-square method, find the vertex of the function f(x) = –2x2 + 12x + 5 and indicate whether it is a minimum or a maximum and at what point.

  10. anonymous
    • one year ago
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    \(f(x)=-2x^2+12x+5\) Group it again \(f(x)=(-2x^2+12x)+5\) This time, because you have -2 in front of x², you have to factor it out. Can you do that?

  11. anonymous
    • one year ago
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    would it be f(x)=-2(x^2+12x)+5

  12. anonymous
    • one year ago
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    no, you have to divide 12 by -2 as well because it's also in parentheses

  13. anonymous
    • one year ago
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    so it would be 6?

  14. anonymous
    • one year ago
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    12/(-2)= -6 So you have \[f(x)=-2(x^2-6x)+5\] Now take the coefficient of x, that's -6. Divide it by 2, the square the result like we did above

  15. anonymous
    • one year ago
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    okay so would it be minimum or maximum?

  16. anonymous
    • one year ago
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    the number in front of x² is negative, so it's a maximum

  17. anonymous
    • one year ago
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    okay so whats the point? (-3,5)?

  18. anonymous
    • one year ago
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    You have to complete the square to find the point

  19. anonymous
    • one year ago
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    If you don't want to do it that way, use \[x=-\frac{ b }{ 2a }\]

  20. anonymous
    • one year ago
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    okay I just reset my exam so now I have different questions

  21. anonymous
    • one year ago
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    ughhhh I need help

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