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MrNebula

  • one year ago

New school year I forgot how to Algebra! Help me to remember!! A ball is thrown into the air with an upward velocity of 28 ft/s. Its height (h) in feet after t seconds is given by the function h = -16t^2 + 28t + 7. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary.

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  1. MrNebula
    • one year ago
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    Don't give me the answer! TEACH ME!

  2. welshfella
    • one year ago
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    Are you famiilar with finding the derivative of a function?

  3. MrNebula
    • one year ago
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    No, if that's how you solve this, I might remember.

  4. welshfella
    • one year ago
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    ok well you can solve it by finding the vertex of the parabola . The raph is a parabola with a maximum value which corresponds to maximum height of the ball

  5. welshfella
    • one year ago
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    |dw:1441993439026:dw|

  6. welshfella
    • one year ago
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    excuse the drawing

  7. MrNebula
    • one year ago
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    Its fine. So do I just fined the coordinates of the tip top of the hill?

  8. welshfella
    • one year ago
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    yea - I'm a bit rusty at this myself I normally would use calculus but lets try it:- convert the formula to vertex form h = - 16t^2 + 28t - 7 = 16(t^2 + 1.75t) - 7 = -16(( t + 0.875)^2 - 0.765625)) - 7 which gives t = 0.875 seconds and vertex = -16*-0.765625 + 7 = 19.25 feet

  9. welshfella
    • one year ago
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    I completed the square on t^2 - 1.75t

  10. MrNebula
    • one year ago
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    Ok, you kinda gave me the answer but ill use what you have as a example template

  11. MrNebula
    • one year ago
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    Thanks dude!

  12. welshfella
    • one year ago
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    thers some typos ther do you want them corrected?

  13. MrNebula
    • one year ago
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    Sure!

  14. MrNebula
    • one year ago
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    The more I go over these problems the more ill remember, sadly everything is still blank XD

  15. welshfella
    • one year ago
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    h = - 16t^2 + 28t + 7 = 16(t^2 - 1.75t) + 7 = -16(( t - 0.875)^2 - 0.765625)) + 7 this gives the time t = 0.875 seconds and the maximum height = -16 * -0.765625 + 7 = 19.25 ft

  16. MrNebula
    • one year ago
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    Thanks again!

  17. welshfella
    • one year ago
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    vertex form is -16(t - 0.875)^2 + 19.25

  18. welshfella
    • one year ago
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    (0.875,19,25) are the coordinates of the vertex

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