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Math Help - Finding unknown constants

  1. #1
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    Red face Finding unknown constants

    Here is another problem from me.

    I tried solving this, and I am thinking that I somehow need to turn this into an equation with some known points and than solve for a,b and c as a simultaneous equation. However, whenever I try to do this I get lost.

    The curve y = ax2 + bx + c passes through the point (1; 2) and is tangent to the line
    y = x at the origin. Find a, b and c

    Thanks to everyone who reads this
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Finding unknown constants

    y=2x^2
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  3. #3
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    Re: Finding unknown constants

    Hi !

    "The curve y = ax + bx + c is tangent to the line y = x at the origin"
    To be tangent at the origin, at least the curve must pass through the point (0; 0). So 0=a^0+b*0+c. Hence c=0
    y= ax+bx.
    The slope is y'(x)=2ax+b. The slope of the line y=x is 1. So, at the origine, 1=2*0+b. Hence b=1
    y = ax+1
    The curve passes through the point (1; 2). So, 2=a*1+1. Hence a=2-1=1
    y = x+x
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