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Math Help - Need help with 2 quadratics problems...

  1. #1
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    Need help with 2 quadratics problems...

    Hello, I need some help with 2 quadratics problems:

    1. Let f, g be distinct quadratics. In how many places can f and g intersect? Give examples of each case. Is anything else possible? Why?

    2. So far we have been finding the vertex of a quadratic f by evaluating h = -b over 2aand k = f(h); find a formula for k in terms of a, b, c.

    Thank you *SO* much for anyones help in advance...
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  2. #2
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    Quote Originally Posted by Andrew00830 View Post
    Hello, I need some help with 2 quadratics problems:

    1. Let f, g be distinct quadratics. In how many places can f and g intersect? Give examples of each case. Is anything else possible? Why?

    sketch two different parabolas in various configurations ... how many ways can you make them intersect (or not)?

    2. So far we have been finding the vertex of a quadratic f by evaluating h = -b over 2aand k = f(h); find a formula for k in terms of a, b, c.

    \textcolor{red}{h = \frac{-b}{2a}}

    \textcolor{red}{f(x) = ax^2 + bx + c}

    find \textcolor{red}{k = f\left(\frac{-b}{2a}\right)}

    ...
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  3. #3
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    Quote Originally Posted by Andrew00830 View Post
    Hello, I need some help with 2 quadratics problems:

    1. Let f, g be distinct quadratics. In how many places can f and g intersect? Give examples of each case. Is anything else possible? Why?

    2. So far we have been finding the vertex of a quadratic f by evaluating h = -b over 2aand k = f(h); find a formula for k in terms of a, b, c.

    Thank you *SO* much for anyones help in advance...
    If you need help visualizing how your first question looks ... try this ... I know it is sloppy, but it should get the idea across
    Attached Thumbnails Attached Thumbnails Need help with 2 quadratics problems...-scan0001-2-.gif  
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  4. #4
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    Would question #2 look like this?

    k=f(h)=f(-b/(2a))=a*(-b/(2a))^2+b*(-b/(2a))+c=(4ac-b^2)/(4a)
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  5. #5
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    Quote Originally Posted by Andrew00830 View Post
    Would question #2 look like this?

    k=f(h)=f(-b/(2a))=a*(-b/(2a))^2+b*(-b/(2a))+c=(4ac-b^2)/(4a)
    looks fine to me.
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