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Math Help - Domain and Range

  1. #1
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    Domain and Range

    Find the domain and range for each quadratic function.

    a. y = x^2 – 6x +5

    b. y = 3x^2 + 2x +9
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by pashah
    Find the domain and range for each quadratic function.

    a. y = x^2 6x +5

    b. y = 3x^2 + 2x +9
    The RHS of both of these are defined for all of \mathbb{R}, so
    their domains are both the set of all real numbers.

    Because these both represent parabolas which go to \infty as x
    goes to \pm \infty, they can take all values greater than teir minimums.

    The minimum of the first occurs when 2x-6=0, which is at
    x=3, where y=-4, so for a. the range is y \ge 4.

    The minimum of the second occurs when 6x+2=0, which is at
    x=-1/3, where y=26/3, so for a. the range is y \ge 26/3.

    RonL
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  3. #3
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    Quote Originally Posted by pashah
    Find the domain and range for each quadratic function.

    a. y = x^2 6x +5
    I do this slight diffrently.
    Rewrite as,
    x^2-6x+(5-y)=0
    Now, you need to find all y such as this quadradic equation has a real solution. That happens when, the discrimanant is non-negative.
    (-6)^2-4(1)(5-y)\geq 0
    Simplify,
    16+4y\geq 0
    Thus,
    4y\geq -16
    Thus,
    y\geq -4
    b. y = 3x^2 + 2x +9
    Proceede the same,
    3x^2+2x+(9-y)=0
    Work with discrimanant,
    (2)^2-4(3)(9-y)\geq 0
    -104+12y\geq0
    12y\geq  104
    y\geq 8.\bar 6
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