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anonymous

  • 4 years ago

A ball in flight is modeled by the function h(t)=-16t²+128t. Find the maximum height and time to get there.

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  1. Mertsj
    • 4 years ago
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    The maximum height will be the y coordinate of the vertex. Can you find that?

  2. anonymous
    • 4 years ago
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    huh?

  3. Mertsj
    • 4 years ago
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    Do you know that the graph of that function is a parabola?

  4. anonymous
    • 4 years ago
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    yes

  5. Mertsj
    • 4 years ago
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    So then you know that it has either a high point or a low point?

  6. anonymous
    • 4 years ago
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    yes

  7. Mertsj
    • 4 years ago
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    which one does this problem have...a high point (maximum) or a low point (minimum)?

  8. anonymous
    • 4 years ago
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    maximum

  9. Mertsj
    • 4 years ago
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    It has a hight point (maximum) because the coefficient of the t^2 term is negative.

  10. Mertsj
    • 4 years ago
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    Do you know that the high point is called the vertex?

  11. anonymous
    • 4 years ago
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    yes

  12. Mertsj
    • 4 years ago
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    Do you know that the vertex is represented by an ordered pair that has an x value and a y value?

  13. anonymous
    • 4 years ago
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    yes

  14. Mertsj
    • 4 years ago
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    Ok. we need to find that highest point (vertex). The x coordinate of the vertex is x=-b/2a Calculate that.

  15. Mertsj
    • 4 years ago
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    \[x=\frac{-128}{2(-16)}=\frac{-128}{-32} = 4\]

  16. Mertsj
    • 4 years ago
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    \[y=-16(4)^2+128(4)= 256\]

  17. Mertsj
    • 4 years ago
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    So the vertex is (4,256) and the maximum height of the ball is 256 feet.

  18. Mertsj
    • 4 years ago
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    And that happens when the time is 4 seconds.

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