Resources tagged with: Quadratic functions and graphs

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There are 17 NRICH Mathematical resources connected to Quadratic functions and graphs, you may find related items under Coordinates, Functions and Graphs.

Broad Topics > Coordinates, Functions and Graphs > Quadratic functions and graphs

Exploring Quadratic Mappings

Age 14 to 16
Challenge Level

Explore the relationship between quadratic functions and their graphs.

Minus One Two Three

Age 14 to 16
Challenge Level

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 ?

Spaces for Exploration

Age 11 to 14

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

Fence It

Age 11 to 14
Challenge Level

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

Parabolas Again

Age 14 to 18
Challenge Level

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

Parabella

Age 16 to 18
Challenge Level

This is a beautiful result involving a parabola and parallels.

Parabolic Patterns

Age 14 to 18
Challenge Level

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.

Guessing the Graph

Age 14 to 16
Challenge Level

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

Which Quadratic?

Age 14 to 18
Challenge Level

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.

Geometric Parabola

Age 14 to 16
Challenge Level

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

' Tis Whole

Age 14 to 18
Challenge Level

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?

Integral Inequality

Age 16 to 18
Challenge Level

An inequality involving integrals of squares of functions.

More Parabolic Patterns

Age 14 to 18
Challenge Level

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.

Consecutive Squares

Age 14 to 16
Challenge Level

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

Converse

Age 14 to 16
Challenge Level

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

Age 16 to 18
Challenge Level

Find a condition which determines whether the hyperbola y^2 - x^2 = k contains any points with integer coordinates.

Janusz Asked

Age 16 to 18
Challenge Level

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?