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Math Help - Mathematics Ib 3283 quadratic question

  1. #1
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    Mathematics Ib 3283 quadratic question

    Find the values of m for which the lines y=mx-2 are tangents to the curve with equation y=x^2-4x+2

    Thanks in advance!

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    Re: Mathematics Ib 3283 quadratic question

    the y-values of a tangent line and curve are equal at the point of tangency, plus their respective slopes are also equal ...
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    Re: Mathematics Ib 3283 quadratic question

    Ok so what does that mean, how would I find m?
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    Re: Mathematics Ib 3283 quadratic question

    Quote Originally Posted by alexj987 View Post
    Ok so what does that mean, how would I find m?
    exactly what I stated:

    y-values are equal ...

    mx-2 = x^2-4x+2

    and slopes are equal ...

    \frac{d}{dx}(mx-2) = \frac{d}{dx}(x^2-4x+2)
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  5. #5
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    Re: Mathematics Ib 3283 quadratic question

    Yes, Ive made the two equations equal each other earlier but still do not fully understand, sorry for being dull ...
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    Re: Mathematics Ib 3283 quadratic question

    have you not solved a system of equations before?

    mx-2 = x^2-4x+2

    m = 2x-4

    substitute (2x-4) for m in the first equation, solve for x, then determine the possible value(s) for m
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    Re: Mathematics Ib 3283 quadratic question

    Did that, factored and got an answer of x=1, then plugged that back into x^2-4x+2 which gives -1
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    Re: Mathematics Ib 3283 quadratic question

    your value of x is incorrect ... check your algebra. Also, you get two possible values for x.
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    Re: Mathematics Ib 3283 quadratic question

    Yes, Im sorry, ok using the quadratic formula, x=1+/-√2
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    Re: Mathematics Ib 3283 quadratic question

    (2x-4)x - 2 = x^2 - 4x + 2

    2x^2 - 4x - 2 = x^2 - 4x + 2

    x^2 - 4 = 0

    try again ...
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