Quadratic functions and graphs

  • More Parabolic Patterns
    problem

    More parabolic patterns

    Age
    14 to 18
    Challenge level
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    The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.
  • Parabolic Patterns
    problem

    Parabolic patterns

    Age
    14 to 18
    Challenge level
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    The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

  • Consecutive Squares
    problem

    Consecutive squares

    Age
    14 to 16
    Challenge level
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    The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
  • Converse
    problem

    Converse

    Age
    14 to 16
    Challenge level
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    Clearly if a, b and c are the lengths of the sides of an equilateral triangle then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true?
  • Grid Points on Hyperbolas
    problem

    Grid points on hyperbolas

    Age
    16 to 18
    Challenge level
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    Find a condition which determines whether the hyperbola y^2 - x^2 = k contains any points with integer coordinates.
  • Janusz asked
    problem

    Janusz asked

    Age
    16 to 18
    Challenge level
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    In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?
  • spaces for exploration
    article

    Spaces for exploration

    Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.