#### You may also like 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. ### Discriminating

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.

# Can You Find ... Cubic Edition

##### Age 16 to 18Challenge Level This resource is from Underground Mathematics.

Can you find a cubic curve that...

(a) ... passes through the $x$-axis at $x=1$ and $x=-1$?

(b) ... passes through the origin and touches the $x$-axis at $x=-3$?

(c) ... touches the $x$-axis at $x=2$ and crosses the $y$-axis at $12$?

(d) ... crosses the $y$-axis at $-6$ and has three integer roots?

(e) ... crosses the $y$-axis at $y=5$ and touches the $x$-axis at $x=1$?

Are any of the curves described above unique?

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.