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Thread: Turning point form not showing correct TP? Important and urgent!

  1. #1
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    Turning point form not showing correct TP? Important and urgent!

    Hey guys,

    so I have the function f(x)= -3x2 - 18x - 26.

    I've put this into TP form and have gotten (x+3)2 - 1/3

    This would lead me to believe that the x turning point is -3 and the y turning point is - 1/3. However, when graphing it using desmos, it shows that the y turning point is 1.

    I thought I did something wrong, but using that turning point form, I found the correct x intercepts, so I'm very confused! Can anyone help?
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  2. #2
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    Re: Turning point form not showing correct TP? Important and urgent!

    $\begin{align*}

    f(x) &= -3x^2 - 18x - 26 \\

    &= -3\left(x^2 +6x + \dfrac{26}{3}\right) \\

    &= -3\left((x+3)^2 - 9 +\dfrac{26}{3} \right) \\

    &= -3\left((x+3)^2 - \dfrac{1}{3}\right) \\

    &= -3(x+3)^2 +1

    \end{align*}$
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  3. #3
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    Re: Turning point form not showing correct TP? Important and urgent!

    Quote Originally Posted by AlwaysHufferr View Post
    so I have the function f(x)= -3x2 - 18x - 26.

    I've put this into TP form and have gotten (x+3)2 - 1/3
    Well, you could have substituted, as example, x=2
    and seen right away your result is not correct...
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  4. #4
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    Re: Turning point form not showing correct TP? Important and urgent!

    Important fact: f(x) and a * f(x) will always have the same x-intercepts and the same x turning points if a is not zero, but will not have the same y-intercept and will not have the same y turning points unless a is 1.
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