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Math Help - constructing polynomials

  1. #1
    Junior Member
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    constructing polynomials

    Qs. Write down a quadratic polynomial with a minimum value of 3 when x=2, and P(0)=15

    im not looking for the answer here, i would jst realli like to no how to get there and the processes of working these kind of questions out
    thanks so much for any help given =D
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by THSKluv View Post
    Qs. Write down a quadratic polynomial with a minimum value of 3 when x=2, and P(0)=15

    im not looking for the answer here, i would jst realli like to no how to get there and the processes of working these kind of questions out
    thanks so much for any help given =D
    assume
     P(x)=ax^2+bx+c

    with conditions given is problem, determine a,b,c.
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by THSKluv View Post
    Qs. Write down a quadratic polynomial with a minimum value of 3 when x=2, and P(0)=15

    im not looking for the answer here, i would jst realli like to no how to get there and the processes of working these kind of questions out
    thanks so much for any help given =D
    The standard for of a quadratic:

    a(x+\frac{b}{2a})^2-\frac{b^2}{4a}+c

    Can you see what needs to be done?
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  4. #4
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    I like the following method better...

    Use the vertex form of the quadratic:
    P(x) = a(x - h)^2 + k
    where (h, k) is the vertex. The vertex is the minimum or maximum value of the parabola, so plug (2, 3) in:
    P(x) = a(x - 2)^2 + 3

    You're also given that P(0) = 15, so plug in 0 for x and 15 for P(x), and solve for a:
    15 = a(0 - 2)^2 + 3
    ...

    I'm sure you can figure out the rest.


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