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Math Help - find b and c

  1. #1
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    find b and c

    Help please.
    Find b and c so that y=13(x^2)+bx+c has a vertex (3,-2).

    so b=______
    and c=_____
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  2. #2
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    Hello, lsnyder!

    Find b and c so that y\:=\:13x^2+bx+c has a vertex (3,-2).
    We're expected to know that the vertex is at: . x \:=\:\frac{-b}{2a}

    So we have: . \frac{-b}{2(13)} \:=\:3 \quad\Rightarrow\quad b \:=\:-78

    . . and the equation is: . y \:=\:13x^2 - 78x + c


    Since (3,-2) is on the graph: . -2 \:=\:13(3^2) - 78(3) + c \quad\Rightarrow\quad c \:=\:115


    Therefore: . \boxed{b \:=\: -78}\quad\boxed{ c \:=\:115}

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