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Thread: ellipse, parabola, hyperbola, analytical geometry

  1. #1 ellipse, parabola, hyperbola, analytical geometry 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    hello to all forum members.

    i recently encountered a new topic, which was on studying further quadratic functions.
    my question here is, about what year level, or grade during high school or pre-uni, do you learn this quadratic equations of different forms of quadratic analysis(ellipse, and hyperbola etc....)????



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  3. #2  
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    Such topics are generally introduced at the pre-calculus level. They are taught along with the conic sections, and than described by what are known as Cartesian equations--named after the founder of analytic geometry, Rene Descartes. Secondly, a hyperbola is not truly the curve of a quadratic equation; although a concave down parabola can indeed be described quadratically, a hyperbola is rather the curve generated by an equation of a negative exponent power, generally x^(-1). At the calculus level the understanding of concavity (and even to some extent monotonicity and convexity) are developed through use of the derivative.


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  4. #3  
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    seems rather quadratic to me, as does
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  5. #4  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    pre-calculus so that would be around the age of 15(that would be my age)?
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    Yes; that would be an appropriate age to introduce the conics.
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  7. #6  
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    Quote Originally Posted by Bender
    seems rather quadratic to me, as does
    Bender, the latter equation is quartic, and in both the of the equations you have put the X and Y values on the same side of the equations--if we view things this way than 0 = mx + b - y is now a quadratic, since it is of degree two, but it is obviously linear.
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  8. #7  
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    Quote Originally Posted by Ellatha
    Quote Originally Posted by Bender
    seems rather quadratic to me, as does
    Bender, the latter equation is quartic, and in both the of the equations you have put the X and Y values on the same side of the equations--if we view things this way than 0 = mx + b - y is now a quadratic, since it is of degree two, but it is obviously linear.
    Wrong.

    Bender is correct in the usual terminology which considers the highest total degree of the expressions that occur in a multivariable polynomial.

    By why argue semantics ?
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    Damn; I made a rather very stupid mistake when recalling the basics of polynomials: for some reason I thought that that degree of a polynomial was determined by the sum of the powers of all of the variables of the polynomial, but now I do recall that you are both correct that it is the highest power of any term in the polynomial (that is the sum of the powers of the variables of a certain term in the polynomial). I apologise to Bender in that case.
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  10. #9  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    ok thank you for all responses
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    We would do an exam called an 'O' level at the age 15-16
    then an A level at 17-18.
    I think they may have been under the A level stuff but I am not 100% sure.

    Here is an A level question about elipses so yes I'd say A level.

    http://www.a-levelmathstutor.com/circles-ellipses.php

    Bit too hard for O level, you get marks there for getting your name and date correct on the paper
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  12. #11  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    oh yes indeed the "O" level.
    i myself at the moment is taking the GCE "O" level mathematics, and a-level maths also. Thats our curriculum (just saying)
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