Find the value of c such that the line with equation y= 2x + c is a tangent to the parabola y = x squared + 3x

Question

Find the value of c such that the line with equation y= 2x + c is a tangent to the parabola y = x squared + 3x

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Faith 1 week 2021-10-07T16:32:25+00:00 1 Answer 0

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    2021-10-07T16:33:56+00:00

    Answer:

    c=-1/4

    Step-by-step explanation:

    Y=2x+c=2(x+c/2), so m=2.

    To be tangent we need to check y’ of parabola: y’=2x+3.

    So for some x it must be 2x+3=2 (cause m=2). We have x=-1/2.

    Now we use x=-1/2 to find y from 2nd equation (equation of parabole): we got y=1/4-3/2=-5/4.

    So tangent has point (-1/2,-5/4).

    Put that point in firts equation (equation of line): -5/4=-1+c,

    so we have c=-1/4.

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45:7+7-4:2-5:5*4+35:2 =? ( )