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Add Maths Formulae List: Form 4 (Update 18/9/08) 01 Functions Absolute Value Function
Inverse Function If
f ( x ), if f ( x ) ≥ 0 f ( x)
y = f ( x ) , then f −1 ( y ) = x
Remember: Object = the value of x Image = the value of y or f(x) f(x) map onto itself means f(x) = x
− f ( x), if f ( x ) < 0
02 Quadratic Equations General Form
Quadratic Formula
ax 2 + bx + c = 0
−b ± b 2 − 4ac x= 2a
where a, b, and c are constants and a ≠ 0. *Note that the highest power of an unknown of a quadratic equation is 2.
When the equation can not be factorized. Nature of Roots
Forming Quadratic Equation From its Roots: If α and β are the roots of a quadratic equation
α +β =−
b a
αβ =
c a
b 2 − 4ac b 2 − 4ac b 2 − 4ac b 2 − 4ac
The Quadratic Equation
x 2 − (α + β ) x + αβ = 0 or x − ( SoR ) x + ( PoR ) = 0 SoR = Sum of Roots PoR = Product of Roots 2
http://www.one-school.net/notes.html
1
>0 =0 <0 ≥0
⇔ two real and different roots ⇔ two real and equal roots ⇔ no real roots ⇔ the roots are real