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Math Help - Calculus Slope Problem (Should be very easy!)

  1. #1
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    Calculus Slope Problem (Should be very easy!)

    Hi all,

    I have the easiest problem ever...and yet I just can't solve it. It furstrates me to the point of wanting to punch the wall, because the problem itself looks so darn easy! It's a homework problem, and I've already done 20 or so problems that are much, much harder. And yet this one problem confounds me to the point of tears. Any help?



    Problem:

    Find a function y = ax^2 + bx + c whose graph has an x-intercept of 1, a y-intercept of -2, and a tangent line with a slope of -1 at the y intercept.



    My work so far:

    At (0, -2), Y' = -X + 2

    Thus, Y - -0.5X^2 + 2X + C

    And C = -2 (Can be figured out from y-intercept)

    But the equation I get isn't right...help
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  2. #2
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    Re: Calculus Slope Problem (Should be very easy!)

    Quote Originally Posted by ohsnapadragon View Post
    Hi all,

    I have the easiest problem ever...and yet I just can't solve it. It furstrates me to the point of wanting to punch the wall, because the problem itself looks so darn easy! It's a homework problem, and I've already done 20 or so problems that are much, much harder. And yet this one problem confounds me to the point of tears. Any help?



    Problem:

    Find a function y = ax^2 + bx + c whose graph has an x-intercept of 1, a y-intercept of -2, and a tangent line with a slope of -1 at the y intercept.



    My work so far:

    At (0, -2), Y' = -X + 2

    Thus, Y - -0.5X^2 + 2X + C

    And C = -2 (Can be figured out from y-intercept)
    So you are saying y= -(1/2)x^2+ 2x- 2. When x= 1, y(1)= -(1/2)+ 2- 2= -1/2, NOT 1 so this does not satisfy "has an x-intercept of 1".
    Your mistake is saying that "at x= (0, -2), Y'= -x+ 2". The equation of the tangent line, at (0, -2), is y= -2x+ 2 but that is NOT the derivative function.

    But the equation I get isn't right...help
    Instead, knowing that y= ax^2+ bx+ c, the fact that this function "has an x-intercept of 1" means that y(1)= a+ b+ c= 1. The fact that the graph has "a y-intercept of -2" means that y(0)= c= -2. The fact that the " tangent line with a slope of -1 at the y intercept" means that y'(0)= 2a(0)+ b= -2 so that b= -2. Put b= c= -2 into a+ b+ c= 1 to find a.
    Last edited by HallsofIvy; September 21st 2013 at 08:51 AM.
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  3. #3
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    Re: Calculus Slope Problem (Should be very easy!)

    Thanks so much!
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