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Math Help - find a function problem

  1. #1
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    find a function problem

    The problem says..

    Q. Find a function y=ax2+bx+c whose graph has an x-intercept of 1, y-intercept of -3, and a tangent line with a slope of 1 at the y-intercept.

    I can't even understand what this question is asking for let alone solving it. Can any one help?

    Thanks!
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  2. #2
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    Re: find a function problem

    y = ax^2+bx + c ------- (1)
    It is given the x intercept is . That means when y = 0 x = 1
    Hence from ( 1 ) we get a + b + c = 0 ----- ( 2 )
    Again we have y intercept = -3. That means when x = 0 y = -3.
    Again from (1) we get c = -3. ------- ( 3 )
    Now it says that the slope of tangent is 1 at y intercept. It means slope of tangent = 1 at ( 0,-3)
    But the slope of tangent to a curve is given by dy/dx. Thus fro ( 1)
    dy/dx = 2ax + b at ( 0,-3 ), dy/dx = 1. Thus we have b = 1 ----- ( 4 )
    Now from (1), (2) and (3) we get a = 2, b=1 and c = -3.
    Thus by plugging in these values in (1) we get the function as
    2x^2 + x 3 = 0
    Thanks from ameerulislam
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  3. #3
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    Re: find a function problem

    We are told to find:

    y(x)=ax^2+bx+c

    where:

    y(0)=-3

    y(1)=0

    y'(0)=1

    From these, you should find 3 linear equations in a,b,c from which you may determine their values. Can you proceed?
    Thanks from ameerulislam
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  4. #4
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    Re: find a function problem

    Quote Originally Posted by ibdutt View Post
    y = ax^2+bx + c ------- (1)
    It is given the x intercept is . That means when y = 0 x = 1
    Hence from ( 1 ) we get a + b + c = 0 ----- ( 2 )
    Again we have y intercept = -3. That means when x = 0 y = -3.
    Again from (1) we get c = -3. ------- ( 3 )
    Now it says that the slope of tangent is 1 at y intercept. It means slope of tangent = 1 at ( 0,-3)
    But the slope of tangent to a curve is given by dy/dx. Thus fro ( 1)
    dy/dx = 2ax + b at ( 0,-3 ), dy/dx = 1. Thus we have b = 1 ----- ( 4 )
    Now from (1), (2) and (3) we get a = 2, b=1 and c = -3.
    Thus by plugging in these values in (1) we get the function as
    2x^2 + x 3 = 0
    Our goal here is to help with the problems, not provide full solutions...giving full solutions is much less helpful than engaging the student in the process.
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  5. #5
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    Re: find a function problem

    when some one asks to find the function this means finding the values of the constants ?
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  6. #6
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    Re: find a function problem

    Quote Originally Posted by ameerulislam View Post
    when some one asks to find the function this means finding the values of the constants ?
    Yes, you could consider the constants the parameters to be found. The quadratic ax^2+bx+c is general, and you are asked to find the one specific quadratic that satisfies the given conditions, which means you need to determine that values of a, b and c.
    Thanks from ameerulislam
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  7. #7
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    Re: find a function problem

    ok what is the reason of saying this line..
    a tangent line with a slope of 1 at the y-intercept. why specific intercept?

    what would have happened if it said
    a tangent line with a slope of 1 at the x-intercept. Or is it even possible?
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: find a function problem

    We know the value of x at the y-intercept, but we don't know the value of x at the x-intercept, as this would depend on the parameters via the quadratic formula.
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  9. #9
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    Re: find a function problem

    Quote Originally Posted by MarkFL View Post
    We know the value of x at the y-intercept, but we don't know the value of x at the x-intercept, as this would depend on the parameters via the quadratic formula.


    Isn't the value of x is given at x-intercept? which is 1 here, right?
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  10. #10
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    Re: find a function problem

    Quote Originally Posted by ameerulislam View Post


    Isn't the value of x is given at x-intercept? which is 1 here, right?
    No, the slope of the tangent line is given as being 1 at the y-intercept, which means we are given:

    \left.\frac{dy}{dx} \right|_{x=0}=1
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  11. #11
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    Re: find a function problem

    Another question:-

    if slope is given let say slope =0

    and y=x^2

    and equation is x^3+y^3-3xy=0

    Can we figure out the the point(s) in the graph where slopes are Zero?

    And the point (0,0) is on which quadrant?
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