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Math Help - Linear Quadratic System

  1. #1
    Senior Member euclid2's Avatar
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    Linear Quadratic System

    Determine the restrictions on the y-intercept so that  y=3x^2+6x-1 intersects with a line with slope 2 in more then one place
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  2. #2
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    skeeter's Avatar
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    let k = y-intercept for the line

    points of intersection can be found by setting the linear and quadratic equations equal to each other ...

    3x^2 + 6x - 1 = 2x + k

    set the equation equal to 0 ...

    3x^2 + 4x - (1+k) = 0

    if the line intersects the parabola twice, then the above quadratic must have two distinct real roots.

    for the quadratic to have two distinct real roots, the discriminant, b^2-4ac > 0

    4^2 - 4(3)[-(1+k)] > 0

    solve the inequality for k.
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