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Math Help - Trig

  1. #1
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    Trig

    A ball is thrown verically upward from the balcony of an apartment building. The ball falls to the ground the height of the ball, h metres, above the ground after t seconds is given by the function: h(t)= -5t^2+15t+45

    I have the factored form or vertex cant remeber which one it is: y=-5(x+2.3)+56.5

    I'm having trouble finding how long it takes the ball to reach the max height. and how high the balcony is
    any help is appreciated thnks
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  2. #2
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    Quote Originally Posted by Gomaz23 View Post
    A ball is thrown verically upward from the balcony of an apartment building. The ball falls to the ground the height of the ball, h metres, above the ground after t seconds is given by the function: h(t)= -5t^2+15t+45

    I have the factored form or vertex cant remeber which one it is: y=-5(x+2.3)+56.5

    I'm having trouble finding how long it takes the ball to reach the max height. and how high the balcony is
    any help is appreciated thnks
    Your vertex form is wrong...How are you getting that?
    Last edited by TheMasterMind; January 25th 2009 at 11:59 AM.
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  3. #3
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    really? well i go tit by factoring the orginal function.
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  4. #4
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    Quote Originally Posted by Gomaz23 View Post
    really? well i go tit by factoring the orginal function.
    ...By completing the square you mean? show me all your steps and then we can work at it
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  5. #5
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    h(t)= -5t^2+15t+45

    next: -5(t^2-3t) (45
    all i did was divide out the 5 and divide the 15 by negative 5 and took out the 45
    next: -3/2=-1.5 -1.5^2= 2.3
    divide negative 3 by 2 then squared the answer
    next: -5(t^2-3t+2.3) -2.3 (-5) (45
    -5(t^2-3t+2.3) 11.5 (45
    i took out the 2.3 then multiplied the negative 5 to it
    Next: -5(t^2-3t+2.3) 56.5
    i added 11.5 to 45
    next: y= -5(x+2.3) +56.5
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  6. #6
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    Quote Originally Posted by Gomaz23 View Post
    h(t)= -5t^2+15t+45

    next: -5(t^2-3t) (45
    all i did was divide out the 5 and divide the 15 by negative 5 and took out the 45
    next: -3/2=-1.5 -1.5^2= 2.3
    divide negative 3 by 2 then squared the answer
    next: -5(t^2-3t+2.3) -2.3 (-5) (45
    -5(t^2-3t+2.3) 11.5 (45
    i took out the 2.3 then multiplied the negative 5 to it
    Next: -5(t^2-3t+2.3) 56.5
    i added 11.5 to 45
    next: y= -5(x+2.3) +56.5
    close

    h(t)-5t^2+15t+45

    =-5(t^2-3t)+45

    =-5(t^2-3t+2.25-2.25)+45

    =-5(t^2-3t)+45+11.25

    <br />
=-5(t-1.5)^2+56.25

    1.5,56.25)" alt="V1.5,56.25)" />
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  7. #7
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    now how do i find how long it takes to reach the max value and how high the balcony is
    Last edited by Gomaz23; January 25th 2009 at 02:27 PM. Reason: typo
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  8. #8
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    Quote Originally Posted by Gomaz23 View Post
    now how do i find how long it takes to reach the max value and how high the balcony is
    I) 1.5 seconds, the x co-ordinate of the vertex

    II)The ball leaves the balcony at t=0

    Thus
    h=-5tsqrd+15+45
    h=-5(0)sqrd+15+45
    =45m

    Therefore the balcony is 45m high
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  9. #9
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    would i need to plug this in to find the time the ball reached that height
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  10. #10
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    Quote Originally Posted by Gomaz23 View Post
    would i need to plug this in to find the time the ball reached that height
    I modified my post, it is 1.5seconds, the y-coordinate, i misread the question at first
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  11. #11
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    o ok thnks a lot
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  12. #12
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    Quote Originally Posted by Gomaz23 View Post
    o ok thnks a lot
    No problem, have a good one
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  13. #13
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    wait one more question howd u get 1.5 for the vertex form
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  14. #14
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    Quote Originally Posted by Gomaz23 View Post
    wait one more question howd u get 1.5 for the vertex form
    when you get to the end which was

    -5(tsqrd-3)+56.25

    you must divide 3 by 2 to yield

    -5(t-1.5)sqrd+56.25

    you will always divide k by 2 for the final in y=a(h-k)+d

    just a rule of completing the square
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