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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.

Problem
Primary curriculum
Secondary curriculum
### What's That Graph?

Can you work out which processes are represented by the graphs?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Minus One Two Three

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 ?

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Spaces for Exploration

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

Age 11 to 14

Problem
Primary curriculum
Secondary curriculum
### Fence It

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parabolas Again

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parabella

This is a beautiful result involving a parabola and parallels.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parabolic Patterns

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.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Guessing the Graph

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Quadratic?

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.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Geometric Parabola

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### ' Tis Whole

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?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Integral Inequality

An inequality involving integrals of squares of functions.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Parabolic Patterns

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.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Consecutive Squares

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Converse

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Grid Points on Hyperbolas

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Janusz Asked

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?

Age 16 to 18

Challenge Level