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
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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