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How to sketch quadratic functions
A guide to sketching quadratic functions in which an animated characters defend their besieged town by using quadratic equations to fire projectiles along parabolic paths. The basic quadratic equation is covered and broken down into sections. Altering the value of each section is shown to change the shape and position of the parabolas. Working with the quadratic formula and using the discriminant to find the roots of an equation is demonstrated. Factorising the equation and finding the turning point or vertex are also worked through.
Discuss with students the different parts of a quadratic equation and how altering each value changes the shape and position of the line it describes. Present students with a set of different equations and have them group the equations into which have maximum or minimum turning points, and which have no real roots, equal real roots or distinct real roots. Expand on how to find the turning point for more difficult equations by completing the square.
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