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Math Help - quadratic equations

  1. #1
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    quadratic equations

    hi, i've got a few questions from my book where i'm sure the answers in the back are wrong. the quadratic is factorised into (x - 2) (x - 1) the parabolas cross the x axis at 2 and 1 it then asks me what shape the graph would be. i would think that it would be an inverted U shape (ie like an "n" shape) but the book says its U shaped. similarly with (x + 3) (x + 4) i would expect the opposite of a U shape but the book says it actually is U shaped. am i wrong?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by mark View Post
    hi, i've got a few questions from my book where i'm sure the answers in the back are wrong. the quadratic is factorised into (x - 2) (x - 1) the parabolas cross the x axis at 2 and 1 it then asks me what shape the graph would be. i would think that it would be an inverted U shape (ie like an "n" shape) but the book says its U shaped. similarly with (x + 3) (x + 4) i would expect the opposite of a U shape but the book says it actually is U shaped. am i wrong?
    Hi mark,

    Using the standard quadratic form:

    y=ax^2+bx+c

    If a > 0, then the parabola opens up.

    If a < 0, then the parabola opens down.

    Your example: y=(x-2)(x-1) would be y=x^2-3x+2.

    Since a = 1, the graph is a parabola that opens upward. The same thing happens with your other example: y=(x+3)(x+4). This becomes y=x^2+7x+12 and since a = 1, opens upward as well.
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  3. #3
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by mark View Post
    hi, i've got a few questions from my book where i'm sure the answers in the back are wrong. the quadratic is factorised into (x - 2) (x - 1) the parabolas cross the x axis at 2 and 1 it then asks me what shape the graph would be. i would think that it would be an inverted U shape (ie like an "n" shape) but the book says its U shaped. similarly with (x + 3) (x + 4) i would expect the opposite of a U shape but the book says it actually is U shaped. am i wrong?
    If the coefficient of the x^2 term is positive, then you have a U shaped parabola (opening upward). If the coefficient of x^2 is negative, you have an inverted U shape. In both your examples the coefficient of x^2 is positive -- try expanding the product in your head.

    Good luck!
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  4. #4
    Senior Member nikhil's Avatar
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    Lightbulb

    (x-2)(x-1)
    so you know that it will be a parabola so it will be some sort of U now
    at x=infinity you will get a positive value and also for x=-infinity you will get a positive value so the graph is such a u that is only above x axis and such a u is U not n.
    similarly you can try for other equation.
    otherwise you may trace the graph using calculus
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