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# Which Quadratic?

**This is an Underground Mathematics resource.**

*Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.*

*Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.*## You may also like

### Powerful Quadratics

### Discriminating

### Factorisable Quadratics

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Age 16 to 18

- Problem
- Student Solutions

What are the key features of a quadratic and what information do you need to be able to identify these for a particular example?

This problem is designed to be tackled in a team of four, working as two pairs. One of the pairs is trying to identify the quadratic on a randomly chosen card. You can download the cards here.

**Instructions**

- To begin, place all of the cards on the table and spend a couple of minutes familiarising yourselves with the types of images and equations that might be chosen.
- Next, one pair takes control of the cards, moving them out of sight from the other pair. They select a card at random. The other pair can now ask up to 8 “yes/no” questions to determine the hidden quadratic. It is important that each pair confers and agrees before asking or answering each question.
- You are permitted a maximum of two guesses at the hidden function, and each guess counts as one of your 8 questions.

**Some things to consider**

- Did you guess the quadratic correctly? If not, what additional information did you need?
- Did you make the most of the information you were given? Could you have avoided asking any of your questions?
- Were your questions clear? Did the other pair understand what you meant? Could you have used mathematical language to improve this?
- Would you ask the same questions next time?

This comes in two parts, with the first being less fiendish than the second. Itâ€™s great for practising both quadratics and laws of indices, and you can get a lot from making sure that you find all the solutions. For a real challenge (requiring a bit more knowledge), you could consider finding the complex solutions.

You're invited to decide whether statements about the number of solutions of a quadratic equation are always, sometimes or never true.

This will encourage you to think about whether all quadratics can be factorised and to develop a better understanding of the effect that changing the coefficients has on the factorised form.