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Powerful Quadratics
This comes in two parts, with the first being less fiendish than the second. It’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.
Factorisable Quadratics
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.
Age 16 to 18
Challenge 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 $x$?
(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 $x$?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.