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Math Help - Quadratics Inequality

  1. #1
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    Quadratics Inequality

    Please help! Mental block!

    Solve the following inequation, expressing your answer in set notation:
    x^2 - x - 5 < 0


    and...

    What is the equation of the porabola that goes through the points:
    (0,0)
    (1,-2)
    (4,4)


    please help~ i'm desperate!
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  2. #2
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    Quote Originally Posted by georgiaaa. View Post
    Please help! Mental block!

    Solve the following inequation, expressing your answer in set notation:
    x^2 - x - 5 < 0
    I like to complete the square for tis one.

    x^2 -x + 1/4 < 5 + 1/4

    (x-1/2)^2 < 21/4

    -sqrt(21)/2< (x-1/2) < sqrt(21)/2

    (1-sqrt(21))/2 < x < (1+sqrt(21))/2
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  3. #3
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    Hello, georgiaaa!

    Solve the following inequation, expressing your answer in set notation:
    . . x - x - 5 .< .0
    Think of it as: .y .= .x - x - 5

    We have an up-opening parabola. .When it is negative?
    . . When it is below the x-axis.

    When does that happen?
    . . Let's find the x-intercepts.
    . . . . . . . . . . . . . . . . . . . . . . __
    . . . . . . . . . . . . . . . . . . 1 √21
    Quadratic Formula: .x .= . ---------
    . . . . . . . . . . . . . . . . . . . . .2

    The expression is negative between those two intercepts.
    . . . . . . __ . . . . . . . . . . . . . __
    . . (1 - √21)/2 .< .x .< .(1 + √21)/2



    What is the equation of the parabola that goes through the points:
    . . (0,0), (1,-2), (4,4)
    The general form of a parabola is: .y .= .ax + bx + c

    Plug in the three points:
    . . .(0,0): .a0 + b0 + c .= .0 . . . c = 0
    . . (1,-2): .a1 + b1 + 0 .= .-2 . . . .a + .b .= .-2 .[1]
    . . .(4,4): .a4 + b4 + 0 .= .4 . . . 16a + 4b .= .4 . [2]

    Divide [2] by 4: . 4a + b .= .1
    . . Subtract [1]: . .a + b .= .-2

    . . and we get: .3a = 3 . . a = 1

    Substitute into [1]: .1 + b .= .-2 . . b = -3


    Therefore, the parabola is: .y .= .x - 3x

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