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help_people

  • one year ago

The function f(t) = t2 + 4t − 14 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work. Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? Part C: Determine the axis of symmetry for f(t).

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  1. help_people
    • one year ago
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    i have all the parts ecvept for a

  2. Astrophysics
    • one year ago
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    So you want to complete the square?

  3. Astrophysics
    • one year ago
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    If you have \[x^2+ax=0\] we can do the following \[x^2+\frac{ 2ax }{ 2 } + \left( \frac{ a }{ 2 } \right)^2-\left( \frac{ a }{ 2 } \right)^2=0\] (complete the square)

  4. Astrophysics
    • one year ago
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    But don't forget about third term, you just add that, so I'll show what I mean by starting it off |dw:1443909088007:dw| now you can factor

  5. Astrophysics
    • one year ago
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    |dw:1443909240041:dw|

  6. help_people
    • one year ago
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    so whats the ansswer and what do you want me to factor?

  7. Astrophysics
    • one year ago
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    \[(t^2+4t+4)-14-4=0\] factor \[(t^2+4t+4)\]

  8. help_people
    • one year ago
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    (t+2)^2 (factor)

  9. Astrophysics
    • one year ago
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    Right so you have \[(t+2)^2-18\]

  10. Jhannybean
    • one year ago
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    \[(t^2+4t)-14\qquad \qquad c=\left(\frac{4}{2}\right)^2 = (\color{red}{2})^2=4 \]\[(t^2+4t+4)-14-4\]\[=(t+\color{red}{2})^2-18\]

  11. Astrophysics
    • one year ago
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    The process above is what is called completing the square, we often use it if we are unable to factor what we have, to check if something if factorable we check the discriminant \[b^2-4ac<0\] see if it's less then 0 it means we cannot factor and have to use complete the square or another method such as quadratic formula.

  12. Jhannybean
    • one year ago
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    The formula for completing the square: \(\left(x\pm \dfrac{b}{2}\right)^2 \pm b^2\pm c\)

  13. Jhannybean
    • one year ago
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    I believe that's it...

  14. help_people
    • one year ago
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    THANKS EVERYBODY: )))))

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