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Math Help - Some more general questions..

  1. #1
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    Some more general questions..

    Hey,

    I have some general questions from "all-around" math:

    • When factoring, why do you have to use perfect squares?
    • Is the equation ax^2+bx+c=0 the same as the equation y=ax^2+bx+c? (referring to quadratics)
    • What does the term "difference of squares" imply?
    • Are there any general rules when factoring trinomials?


    Thanks everyone.
    -NineZeroFive
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  2. #2
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    This,
    ax^2+bx+c=0 is an equation. Meaning it has to be solved.

    This,
    ax^2+bx+c=y is a function. It represents the relationship between the x-coordinate and y-coordinate.
    ---
    Diffrence of square means,
    x^2-y^2 and they can always be factored.
    (x+y)(x-y)
    ---
    Why use perfect squares?
    You mean why bring everything to perfect square in a conic? Because after you used perfect squares the shape of the conic is easily recognizable. And also it can be graphed easily by simply doing a translation of the axes.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker
    This,
    ax^2+bx+c=0 is an equation. Meaning it has to be solved.

    This,
    ax^2+bx+c=y is a function. It represents the relationship between the x-coordinate and y-coordinate.
    ---
    Diffrence of square means,
    x^2-y^2 and they can always be factored.
    (x+y)(x-y)
    ---
    Why use perfect squares?
    You mean why bring everything to perfect square in a conic? Because after you used perfect squares the shape of the conic is easily recognizable. And also it can be graphed easily by simply doing a translation of the axes.

    Thanks for the FAST reply!

    I mean..why must we use perfect squares when factoring? :S
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  4. #4
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    Also, what is the x intercept(s) and y intercept of y=x^2? I'm pretty sure I have the correct answer, just want to confirm because the answer on the back of the textbook I'm using seems 'wierd'. It says the x-intercept is 12 (??) and y inctercept is 0 (which I understand).

    Can someone please use the Quadractic formula to figure out the x-intercept(s) of the above equation, if there are any?


    Thanks again,
    -NineZeroFive
    Last edited by NineZeroFive; July 18th 2006 at 01:04 PM.
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  5. #5
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    The x-intercept would be where the graph crosses/touches the x-axis. Thus at this point y=0. So this occurs when 0=x^2, obviously at 0.

    The y-intercept would be where the graph crosses/touches the y-axis. Thus at this point x=0. So this occurs when y=0^2, or 0.
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  6. #6
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    Quote Originally Posted by Jameson
    The x-intercept would be where the graph crosses/touches the x-axis. Thus at this point y=0. So this occurs when 0=x^2, obviously at 0.

    The y-intercept would be where the graph crosses/touches the y-axis. Thus at this point x=0. So this occurs when y=0^2, or 0.
    Thats, what I thought, Thanks, I guess I'll have to ask the teacher tomorrow.

    Three more questions: (both referring to parabolas)

    If an expression is in the form of ax^2+bx+c, and the question asks you to find the y-intercept, how would you do so?

    Also, when using the Quadratic formula, how to you know when there is only 1 x-intercept instead of the usual 2?

    Can someone please use the Quadractic formula to figure out the x-intercept(s) of the equation y=x^2, if there are any?

    Thanks alot.
    -NineZeroFive
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  7. #7
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    Quote Originally Posted by NineZeroFive
    Thats, what I thought, Thanks, I guess I'll have to ask the teacher tomorrow.

    Three more questions: (both referring to parabolas)

    If an expression is in the form of ax^2+bx+c, and the question asks you to find the y-intercept, how would you do so?
    solve for x=0
    Also, when using the Quadratic formula, how to you know when there is only 1 x-intercept instead of the usual 2?
    there is a thing called the discriminant b^2-4ac (it is the thing under the radical in the quadratic formula) if the discriminant is negative there is no x-intercept, if positive there are 2 x-intercepts, and if it equals 0 than there is 1 x-intercept.


    x=\frac{\neg b\pm\sqrt{\bold{b^2-4ac}}}{2a}
    (the discriminant is bold)
    Can someone please use the Quadractic formula to figure out the x-intercept(s) of the equation y=x^2, if there are any?

    Thanks alot.
    -NineZeroFive
    write out the equation in full...
    y=ax^2+bx+c\quad\Rightarrow\quad 0=1x^2+0x+0

    than solve...

    x=\frac{\neg b\pm\sqrt{b^2-4ac}}{2a}

    x=\frac{\neg 0\pm\sqrt{0^2-4(1)(0)}}{2(1)}

    x=\frac{\pm\sqrt{0}}{2} the discriminant is 0, therefore we know there is only 1 solution.

    ~ Q\!u\!i\!c\!k
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  8. #8
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    Quote Originally Posted by Quick
    solve for x=0
    there is a thing called the discriminant b^2-4ac (it is the thing under the radical in the quadratic formula) if the discriminant is negative there is no x-intercept, if positive there are 2 x-intercepts, and if it equals 0 than there is 1 x-intercept.


    x=\frac{\neg b\pm\sqrt{\bold{b^2-4ac}}}{2a}
    (the discriminant is bold)

    write out the equation in full...
    y=ax^2+bx+c\quad\Rightarrow\quad 0=1x^2+0x+0

    than solve...

    x=\frac{\neg b\pm\sqrt{b^2-4ac}}{2a}

    x=\frac{\neg 0\pm\sqrt{0^2-4(1)(0)}}{2(1)}

    x=\frac{\pm\sqrt{0}}{2} the discriminant is 0, therefore we know there is only 1 solution.

    ~ Q\!u\!i\!c\!k

    Thanks ALOT Quick. YOU ARE AMAZING!!

    BTW: Your PM inbox is full.
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  9. #9
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    Quote Originally Posted by NineZeroFive
    Three more questions: (both referring to parabolas)
    This is one of the funniest mistakes in grammar I've ever seen.

    Also, I wanted to say that when factoring you don't need to make things into perfect squares, it's just a convenient thing to do.
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  10. #10
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    Quote Originally Posted by NineZeroFive
    Hey,

    I have some general questions from "all-around" math:

    • Are there any general rules when factoring trinomials?


    Thanks everyone.
    -NineZeroFive
    Yes, but they're merely "tricks" to help you factor.

    when given an expression in the form x^2+bx+c the factors will be in the form (x+d)(x+g)

    when given an expression in the form x^2-bx+c the factors will be in the form (x-d)(x-g)

    when given an expression in the form x^2+bx-c the factors will be in the form (x+d)(x-g) where d>g

    when given an expression in the form x^2-bx-c the factors will be in the form (x+d)(x-g) where d<g
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