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Math Help - Quadratic Polynomial

  1. #1
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    Quadratic Polynomial

    Find the quadratic polynomial whose graph passes through the points (0,0) (-1,1) and (1,1).
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Quadratic Polynomial

    x^2
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  3. #3
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    Re: Quadratic Polynomial

    Thanks Dave, how did you arrive at that answer?
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  4. #4
    Senior Member jakncoke's Avatar
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    Re: Quadratic Polynomial

    I used solved the linear system 0 = f(0) = a_3 1 = f(-1) = a_2 - a_1 + a_0 1 = f(1) = a_2 + a_1 + a_0 .
    Then i looked at the question, the points and slapped my self on my forehead and erased all my work to save embarrassment.
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  5. #5
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    Re: Quadratic Polynomial

    Any "quadratic polynomial" can be written in the form y= ax^2+ bx+ c for some numbers, a, b, and c. When x= 0, y= 0 so 0= a(0^2)+ b(0)+ c so c= 0. Then when x= -1, y= 1 so 1= a(-1)^2+ b(-1) or a- b= 1. Finally, when x= 1, y= 1 so 1= a(1)^2+ b(1) or a+ b= 1.

    Solve the two equations a+ b= 1 and a- b= 1 for a and b.
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