Quadratic functions and graphs

There are 17 NRICH Mathematical resources connected to Quadratic functions and graphs

problem

Favourite

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?

problem

Favourite

What's that graph?

Age

14 to 18

Challenge level

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

problem

Favourite

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.

problem

Favourite

Parabella

Age

16 to 18

Challenge level

This is a beautiful result involving a parabola and parallels.

problem

Favourite

Parabolas again

Age

14 to 18

Challenge level

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

problem

Favourite

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 ?

problem

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?

problem

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.

problem

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?

problem

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?

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Quadratic functions and graphs

Fence it

What's that graph?

Parabolic patterns

Parabella

Parabolas again

Minus one two three

Janusz asked

Grid points on hyperbolas

Converse

Consecutive squares