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Resources tagged with Quadratic functions similar to Converse:

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Broad Topics > Sequences, Functions and Graphs > Quadratic functions

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Converse

Stage: 4 Challenge Level: Challenge Level:1

Clearly if a, b and c are the lengths of the sides of a triangle and the triangle is equilateral then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true, and if so can you prove it? That is if. . . .

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Geometric Parabola

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.

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Consecutive Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

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' Tis Whole

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?

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Exploring Quadratic Mappings

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between quadratic functions and their graphs.

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Parabolic Patterns

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

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Parabolas Again

Stage: 4 and 5 Challenge Level: Challenge Level:1

Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?

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Alison's Mapping

Stage: 4 Challenge Level: Challenge Level:1

Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

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More Parabolic Patterns

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

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More Quadratic Transformations

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Here are some more quadratic functions to explore. How are their graphs related?

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Spaces for Exploration

Stage: 3 and 4

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

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Quadratic Transformations

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the two quadratic functions and find out how their graphs are related.

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Minus One Two Three

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?

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Fence It

Stage: 3 Challenge Level: Challenge Level:1

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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Which Quadratic?

Stage: 4 and 5 Challenge Level: Challenge Level:1

This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.

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Guessing the Graph

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?