Page 13 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Quadratic Functions

a  0 and b  0 The vertex of the f(x)
graph is on the right
side of y-axis. 0 x
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Only the b = 0 b > 0
value of b a  0 and b  0 The vertex of the
Form 4 changes graph is on the left f(x) x
side of y-axis.
0

b < 0 b = 0
c  0 The shape of the graph does not change but
the graph moves vertically upwards.
f(x)
f(x) c > 0
c > 0
x
c = 0 0
c = 0
Only the 0 x
value of c
changes c  0 The shape of the graph does not change but
the graph moves vertically downwards.
f(x) f(x)
x
c = 0 0
c = 0
x
0
c < 0 c < 0

2. Discriminant b – 4ac  0 b – 4ac = 0 b – 4ac  0
2
2
2
Two different real Two equal real roots No real roots
Type of roots
roots
a  0 a  0 a  0 a  0 a  0 a  0
a > 0 a < 0 a > 0 a < 0 a > 0 a < 0
x x
x x
Position of the x x
graph of f(x)
The graph intersects The graph touches The graph does not
x-axis at two x-axis at one point intersect or touch
different points. only. x-axis.

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