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Thread: Identifying polynomial variables

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    Question Identifying polynomial variables

    Hi,

    I hope someone can help. I'm trying to solve for the following problem:

    Identifying polynomial variables-screen-shot-2017-08-17-1.17.17-pm.png

    So far I have identified the value for c, which is 1. And then I plugged in the points (3,12) in order to isolate a and b. As follows:

    Identifying polynomial variables-20930628_1504249926297763_1058304670_o.jpg

    I'm struggling to solve for a and b. When I sub a into b, or visa versa, I don't get an actual number. Could someone please go through the steps on how to solve for these two variables? According to the textbook, the solution for a = -11/9 and b = 22/3.

    - Olivia
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    Re: Identifying polynomial variables



    $y=a(x-h)^2+k$

    vertex at $(3,12)=(h,k)$

    $y=a(x-3)^2+12$

    $(0,1)$ is the y-intercept ...

    $1=a(0-3)^2+12 \implies a=-\dfrac{11}{9}$

    $y=-\dfrac{11}{9}(x-3)^2+12$

    expand and collect like terms on the right side to determine the coefficients $b$ and $c$
    Thanks from otownsend
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    Re: Identifying polynomial variables

    Quote Originally Posted by otownsend View Post
    Click image for larger version. 

Name:	Screen Shot 2017-08-17 at 1.17.17 PM.png 
Views:	19 
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ID:	37991
    So far I have identified the value for c, which is 1. And then I plugged in the points (3,12) in order to isolate a and b. As follows:
    Click image for larger version. 

Name:	20930628_1504249926297763_1058304670_o.jpg 
Views:	8 
Size:	371.7 KB 
ID:	37992
    I'm struggling to solve for a and b. When I sub a into b, or visa versa, I don't get an actual number. Could someone please go through the steps on how to solve for these two variables? According to the textbook, the solution for a = -11/9 and b = 22/3.
    You posted this as a calculus question.
    So the derivative, $2ax+b=0)$ at $(3,12)$.
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