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There are **38** NRICH Mathematical resources connected to **Quadratic equations**, you may find related items under Algebraic expressions, equations and formulae.

Problem
Primary curriculum
Secondary curriculum
### Quadratic Patterns

Surprising numerical patterns can be explained using algebra and diagrams...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Partly Circles

What is the same and what is different about these circle questions? What connections can you make?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Interactive Number Patterns

How good are you at finding the formula for a number pattern ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Power Quady

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

Age 16 to 18

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Proof Sorter - Quadratic Equation

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Old Am I?

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square Mean

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Third of the Area

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?

Age 14 to 16

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Mega Quadratic Equations

What do you get when you raise a quadratic to the power of a quadratic?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bird-brained

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Symmetrically So

Exploit the symmetry and turn this quartic into a quadratic.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quad Solve

Can you solve this problem involving powers and quadratics?

Age 16 to 18

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Erratic Quadratic

Can you find a quadratic equation which passes close to these points?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Implicitly

Can you find the maximum value of the curve defined by this expression?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Resistance

Find the equation from which to calculate the resistance of an infinite network of resistances.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plus or Minus

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Golden Mathematics

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Golden Eggs

Find a connection between the shape of a special ellipse and an infinite string of nested square roots.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Construction

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polar Flower

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Fibs

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Xtra

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Halving the Triangle

Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pentakite

Given a regular pentagon, can you find the distance between two non-adjacent vertices?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Many Balls?

A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Ratio

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Continued Fractions II

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Pent

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pareq Calc

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel lines are 1 unit and 2 units.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Target Six

Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Kissing

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Cubes

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]

Age 14 to 16

Challenge Level