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anonymous

  • one year ago

The function f(x) = −x2 + 50x − 264 models the profit, in dollars, a yoga studio makes for selling monthly memberships, where x is the number of memberships sold and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)

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  1. anonymous
    • one year ago
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    medal

  2. freckles
    • one year ago
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    \[f(x)=-x^2+50x-264 \\ \text{ factor } -1 \text{ from the first two terms } \\ f(x)=-(x^2-50x)-264 \\ \text{ now I'm going to leave a little space in the ( )} \\ \text{ this space will be the number we put into complete the square } \\ \text{ but whatever I add in } \\ \text{ I have to subtract out } \\ f(x)=-(x^2-50x+?)-264+? \\ \text{ notice I added in a zero } -?+?=0\]

  3. freckles
    • one year ago
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    now it is time to figure what number that ? should be

  4. freckles
    • one year ago
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    do you know how to complete the square?

  5. anonymous
    • one year ago
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    kinda

  6. freckles
    • one year ago
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    okay so what number should the ? be

  7. freckles
    • one year ago
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    hint: \[x^2+kx+(\frac{k}{2})^2 \text{ is equal to } (x+\frac{k}{2})^2 \]

  8. anonymous
    • one year ago
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    2 ?

  9. anonymous
    • one year ago
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    am i right

  10. anonymous
    • one year ago
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    hello?

  11. freckles
    • one year ago
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    hmm... how did you get that?

  12. anonymous
    • one year ago
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    when you complete a square arent you suposed to add in a 2

  13. freckles
    • one year ago
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    did you read this? \[x^2+kx+(\frac{k}{2})^2 \text{ is equal to } (x+\frac{k}{2})^2 \\ \]

  14. freckles
    • one year ago
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    \[x^2-50x+... \text{ is the same as } x^2+kx... \text{ when } k=-50 \\ x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \\ x^2-50x+...=(x+..)^2 \\ \]

  15. freckles
    • one year ago
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    I left those spaces for you what number should be in place of first space, the space that has 3 dots in it

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