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Math Help - PLEASE HELP! I dont fully understand how to do this certain problem.

  1. #1
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    PLEASE HELP! I dont fully understand how to do this certain problem.

    Graph: y=f(x)=-x2+3x. Give the coordinates of the vertex, the x-intercepts (if they exist), the y-intercept, the domain, range, max/min value, and the equation of the axis of symmetry.

    vertex
    x-int.
    y-int.
    domain
    range
    max/min
    axis of symmetry
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Jluse7 View Post
    Graph: y=f(x)=-x2+3x. Give the coordinates of the vertex, the x-intercepts (if they exist), the y-intercept, the domain, range, max/min value, and the equation of the axis of symmetry.

    vertex
    x-int.
    y-int.
    domain
    range
    max/min
    axis of symmetry
    Hi Jluse7,

    You need to translate your functional notation into vertex form. The graph will be a parabola opening downward.

    f(x)=-x^2+3x

    f(x)=-(x^2-3x)

    Complete the square:

    f(x)=-\left(x^2-3x{\color{red}+\frac{9}{4}}\right){\color{red}+\fr  ac{9}{4}}

    f(x)=\left(x-\frac{3}{2}\right)^2+\frac{9}{4}

    This tells you that the vertex of your parabola is at \left(\frac{3}{2}, \frac{9}{4}\right)

    Set f(x) = 0 to find your x intercepts. Use your original function.

    f(x)=-x^2+3x=0

    -x(x-3)=0

    x=0 \ \ or \ \ x=3

    Notice, since x = 0, f(0) = 0, thus the y-intercept is 0.

    The domain will be all real numbers. There are no restrictions on x.

    The range will be \left\{y|y \le \tfrac{9}{4}\right\}

    The maximum value will occur at the vertex where y=\frac{9}{4}.

    There is no minimum.

    The axis of symmetry is x=\frac{3}{2}. This is a vertical line which passes through the vertex.
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