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C1 Quadratic Functions

 

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 = ax2 + bx + c               where a, b, and c are constants and a ≠ 0

Methods of solving quadratic equations

1) Factorising

2) Completing the square

x2 + bx = (x + b/2)2 – (b/2)2

3) Using the quadratic formula

x =  [-b ±√(b2 – 4ac)]/2a

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

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, b2 – 4ac, which will tell you what roots the equation has

Roots of a quadratic equation

A quadratic equation has:

equal roots when b2 = 4ac (ie when b2 – 4ac = 0)

real roots when b2 ≥ 4ac (ie when b2 – 4ac ≥ 0)

real different roots when b2 > 4ac (ie when b2 – 4ac > 0)

no real roots when b2 < 4ac (ie when b2 – 4ac < 0)

 

 

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