You should know all of the information given below. None of this is given in the Formulae Booklet so you need to remember it.

**The general form of a quadratic equation is**

y = ax^{2} + bx + c where a, b, and c are constants and a ≠ 0

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**Methods of solving quadratic equations**

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1) Factorising

2) Completing the square

x^{2} + bx = (x + b/2)^{2} – (b/2)^{2}

3) Using the quadratic formula

x = [-b ±√(b^{2} – 4ac)]/2a

A quadratic equation has two solutions, and the solutions may be equal

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**Sketching a quadratic graph**

What shape is it?

If a > 0 then the graph is U shaped

If a < 0 then the graph is upside down U shaped

Work out where the graph will cross the axes, ie work out the co-ordinates of the points where x = 0 and y = 0

Work out the value of the discriminant, b^{2} – 4ac, which will tell you what roots the equation has

**Roots of a quadratic equation**

A quadratic equation has:

equal roots when b^{2} = 4ac (ie when b^{2} – 4ac = 0)

real roots when b^{2} ≥ 4ac (ie when b^{2} – 4ac ≥ 0)

real different roots when b^{2} > 4ac (ie when b^{2} – 4ac > 0)

no real roots when b^{2} < 4ac (ie when b^{2} – 4ac < 0)

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