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Math Help - Quadradics equations and inequalities

  1. #1
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    Quadradics equations and inequalities

    Hi, I've got a review sheet due Monday in algebra and I really need some help with it!

    Use quadratic formula to solve:
    0=x(squared)-5x+6
    0=x(squared)+x-10

    Estimate the roots of the equation:
    y=x(squared)-2x-8
    y=x(squared)-4

    Graph:

    y>or equal to x(squared)
    y<x(squared)-3

    Hope I made that clear enough! Thanks!!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Lukeh View Post
    Hi, I've got a review sheet due Monday in algebra and I really need some help with it!

    Use quadratic formula to solve:
    0=x(squared)-5x+6
    0=x(squared)+x-10

    Estimate the roots of the equation:
    y=x(squared)-2x-8
    y=x(squared)-4

    Graph:

    y>or equal to x(squared)
    y<x(squared)-3

    Hope I made that clear enough! Thanks!!!
    without LaTex, we write x squared as x^2

    x^2-5x+6 = 0
    you don't need the quadratic formula for this, but since you asked.

    remember the quadratic formula.
    for a quadratic ax^2 + bx + c = 0, x is given by:

    x = [-b +/- sqrt(b^2 - 4ac)]/2a

    x^2-5x+6 = 0
    => x = [5 +/- sqrt(25 - 4(6)]/2
    => x = [5 +/- sqrt(1)]/2
    => x = (5 + 1)/2 or (5 - 1)/2

    so x = 3 , x = 2


    x^2+x-10 = 0
    x = [-1 +/- sqrt(1 - 4(-10))]/2
    => x = [-1 +/- sqrt(41)]/2
    => x = [-1 + sqrt(41)]/2 or x = [-1 - sqrt(41)]/2

    y=x^2-2x-8
    for the roots, we want x^2 - 2x - 8 = 0
    => (x - 4)(x + 2) = 0
    => x = 4 or x = -2 ...........these are the roots

    y=x^2-4
    this is the difference of two squares

    we have
    y = x^2 - 2^2
    => y = (x + 2)(x - 2)
    for roots, we want
    (x + 2)(x - 2) = 0

    so x = -2 or x = 2


    graph y>or equal to x^2
    i'll get back to you on this

    graph y<x^2-3
    i'll get back to you on this as well
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Lukeh View Post
    Graph:

    y>or equal to x(squared)
    y<x(squared)-3
    the shaded regions are what you want

    the first graph is y >= x^2, in this graph, the line is included

    the second graph is y < x^2 - 3, in this graph, the line is not included so you should draw a broken line.
    Attached Thumbnails Attached Thumbnails Quadradics equations and inequalities-xsq.jpg   Quadradics equations and inequalities-xsq2.jpg  
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  4. #4
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    Thanks a ton.
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