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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 $x$?