Quadratic equations

There are 39 NRICH Mathematical resources connected to Quadratic equations
Quadratic Patterns
problem
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Quadratic patterns

Age
14 to 16
Challenge level
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Surprising numerical patterns can be explained using algebra and diagrams...

Partly Circles
problem
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Partly circles

Age
14 to 16
Challenge level
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What is the same and what is different about these circle questions? What connections can you make?
Power Quady
problem
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Power quady

Age
16 to 18
Challenge level
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Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.
Golden Thoughts
problem
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Golden thoughts

Age
14 to 16
Challenge level
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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.
In Between
problem
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In between

Age
16 to 18
Challenge level
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Can you find the solution to this algebraic inequality?
Square Mean
problem
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Square mean

Age
14 to 16
Challenge level
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Is the mean of the squares of two numbers greater than, or less than, the square of their means?
Always Two
problem
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Always two

Age
14 to 18
Challenge level
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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.

How old am I?
problem
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How old am i?

Age
14 to 16
Challenge level
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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?
Interactive Number Patterns
problem
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Interactive number patterns

Age
14 to 16
Challenge level
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How good are you at finding the formula for a number pattern ?

Placeholder: several colourful numbers
problem

Bird-brained

Age
16 to 18
Challenge level
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How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.