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Math Help - Converting Complex Trinomials into Vertex Form

  1. #1
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    Converting Complex Trinomials into Vertex Form

    I need some help factoring part of an equation.

    How would I factor -5(t2 - 7t + 49/4). I do believe I have to factor it as a fraction but I have no clue what the fraction should be 2ab should equal -7t and b2
    is supposed to equal 49/4.

    My guess is.. -5(t - 7/2)2 Is that correct?? Since technically 7/2 is 3.5.. And 3.5 x 2 = 7.. And then 7/22 should equal 49/4.
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    Re: Converting Complex Trinomials into Vertex Form

    Quote Originally Posted by IvoryChan View Post
    I need some help factoring part of an equation.

    How would I factor -5(t2 - 7t + 49/4). I do believe I have to factor it as a fraction but I have no clue what the fraction should be 2ab should equal -7t and b2
    is supposed to equal 49/4.

    My guess is.. -5(t - 7/2)2 Is that correct?? Since technically 7/2 is 3.5.. And 3.5 x 2 = 7.. And then 7/22 should equal 49/4.
    Why guess? FOIL it out to check your answer. Which is more or less what you did. So you know you have the correct answer.

    -Dan
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    Re: Converting Complex Trinomials into Vertex Form

    I would suggest for easy calculation just take LCM inside the braces and get rid of the denominator.
    -5( t^2 - 7t + 49/4 ) = -5 [ ( 4t^2 - 28t + 49 )/4 ] = -5/4 ( 4t^2 - 28t + 49 ) . Now proceed with the steps for splitting the middle term
    product of coefficient of x^2 and constant term = 4 * 49 = 2 * 2 * 7 * 7 = 14 * 14 = - 14 * - 14 Now we observe that the sum of these factors is indeed -28
    Let us split the middle term
    -5/4 ( 4t^2 - 28t + 49 ) = -5/4 ( 4t^2 - 14t - 14 t + 49 ) = -5/4 [ 2t ( 2t - 7 ) - 7 ( 2t - 7 ) ] = - 5/4 ( 2t-7 ) ( 2t - 7 ) = -5/4 ( 2t-7)^2
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