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 ... Asymptote Edition

Age 16 to 18Challenge Level
Here are some things to think about...

(a) What does a curve with real roots look like algebraically?

(b) What does a curve with vertical asymptotes look like algebraically?

(c) What function does the middle portion of the picture remind you of?

(d) What is happening to $f(x)$ for large, respectively small, values of $x$?