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Math Help - Math 11-Equation of Quadratic Function, when given vertex and other point on parabola

  1. #1
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    Question Math 11-Equation of Quadratic Function, when given vertex and other point on parabola

    Hi! I have this Math 11 problem. I do my math through Distance Ed. and there are no examples like this one in the supplied lessons. If anyone could help me with this question, that would be great!
    The problem statement, all variables and given/known data

    Find the equation of the quadratic function with a vertex at (1,3) passing through the points (2,1). Write your answer in the form y=ax^2+bx+c.


    The attempt at a solution

    Using these two points (one being the vertex), I am able to write an equation, but in the form of y=a(x-h)+k. Below is the answer I get for that:
    y=-2(x-1)+3
    However, I was wondering if I can just convert this answer to the other quadratic form, or do I have to do the question an entirely different way.
    Any comments/help on ways to do this question appreciated.
    Thanks,
    MastiffLover48
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by MastiffLover48 View Post
    Hi! I have this Math 11 problem. I do my math through Distance Ed. and there are no examples like this one in the supplied lessons. If anyone could help me with this question, that would be great!
    The problem statement, all variables and given/known data

    Find the equation of the quadratic function with a vertex at (1,3) passing through the points (2,1). Write your answer in the form y=ax^2+bx+c.


    The attempt at a solution

    Using these two points (one being the vertex), I am able to write an equation, but in the form of y=a(x-h)+k. Below is the answer I get for that:
    y=-2(x-1)+3
    However, I was wondering if I can just convert this answer to the other quadratic form, or do I have to do the question an entirely different way.
    Any comments/help on ways to do this question appreciated.
    Thanks,
    MastiffLover48
    What you have got is a straight line.

    You are required to find y=ax^2+bx+c
    and you are given only two points...hence it is difficult to determine a,b, and c.

    But it is given that (1,3) is a vertex point. Do you know what does it mean?
    At vertex, x=-b/2a......................(1)
    .....do you have any idea about this?

    With the help of eq(1) and another point(2,1), you easily find a,b and c.
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  3. #3
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    Hi MastiffLover48

    The equation should be : y=a(x-h)^2+k
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  4. #4
    Super Member malaygoel's Avatar
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    Quote Originally Posted by songoku View Post
    Hi MastiffLover48

    The equation should be : y=a(x-h)^2+k
    here (h,k) is the vertex.
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  5. #5
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    Hi! Thanks for all the comments! I used the equation that I had:
    y=-2(x-1)^2+3
    and then factored it, which I ended up with an answer of:
    y=-2x^2+4x+1
    Does that seem correct to you?
    Thanks,
    MastiffLover48
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  6. #6
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    Hi MastiffLover48
    Quote Originally Posted by MastiffLover48 View Post
    Hi! Thanks for all the comments! I used the equation that I had:
    y=-2(x-1)^2+3
    and then factored it, which I ended up with an answer of:
    y=-2x^2+4x+1
    Does that seem correct to you?
    Thanks,
    MastiffLover48
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