Spm-Add-Maths-Formula-List-Form4

General Form
f ( x) = ax + bx+ c
where a, b, and c are constants and a ≠ 0.
*Note that the highest power of an unknown of a
quadratic function is 2.
a > 0 ⇒ minimum ⇒ ∪ (smiling face)
a < 0 ⇒ maximum ⇒ ∩ (sad face)
Quadratic Inequalities
a > 0 and f( x ) > 0 a > 0 and f( x ) < 0
a b
a
b
x < a or x> b
a< x< b
http://www.one-school.net/notes.html
2
03 Quadratic Functions
2
Completing the square:
f ( x) = a( x+ p) + q
ONE-SCHOOL.NET
(i) the value of x, x =− p
(ii) min./max. value = q
(iii) min./max. point = ( − p, q)
(iv) equation of axis of symmetry, x = − p
Alternative method:
f ( x) = ax + bx+ c
(i)
b
the value of x, x =−
2a
(ii)
b
min./max. value = f ( − )
2a
(iii) equation of axis of symmetry,
Nature of Roots
2
2
x =−
b
2a
2
b − 4 ac>
0 ⇔ intersects two different points
− =
at x-axis
⇔ touch one point at x-axis
2
b 4 ac 0
04 Simultaneous Equations
To find the intersection point ⇒ solves simultaneous equation.
Remember: substitute linear equation into non- linear equation.
2
b − 4 ac<
0 ⇔ does not meet x-axis