Page 22 - Focus SPM KSSM Tg 4.5 - Add Maths

Additional Mathematics SPM Chapter 2 Quadratic Functions

When the value of a changes, the shape and width of the graph will
change but the axis of symmetry is unchanged. REMEMBER!
The minimum or maximum
value remain unchanged.

For the case of a . 0: For the case of a  0:
• the shape of the graph is and it has a • the shape of the graph is and it has a
minimum point. maximum point
• a . 1 and the larger the value of a, the width of • a . 1 and the larger the value of a, the width of
the graph decreases. the graph decreases.
• 0  a  1 and the smaller the value of a, the • 0  a  1 and the smaller the value of a, the Form 4
width of the graph increases. width of the graph increases.

The vertical line which is passing through the vertex of the graph divides the graph into two
symmetrical parts. Therefore, the equation of the axis of symmetry of the graph for the quadratic
function is given by x = h.

f(x) f(x)
x = h x = h
x
Only Shift to the 0 Shift to the
the left as the right as the
value value of h value of h
decrease
increases
of h Shift to the 0 Shift to the x
changes left as the left as the x = h x = h
value of h value of h
decreases increases
When h changes, the shape of the graph is unchanged but the REMEMBER!
vertex of the graph or the axis of symmetry
• is shifted to the right when the value of h increases. The minimum or maximum
• is shifted to the left when the value of h decreases. value remain unchanged.

Shift upwards f(x) Shift upwards f(x)
as the k > 0 as the value
value of k of k k > 0
increases
k = 0 increases
x
0
x Shift downwards k = 0
Only 0 as the value
the Shift downwards k < 0 of k
value as the value of decreases k < 0
k decreases
of k
changes
When k changes, the shape of the graph is unchanged
but the vertex of the graph REMEMBER!
• is shifted upwards when the value of k increases. • The axis of symmetry is unchanged.
• is shifted downwards when the value of k decreases. • The minimum or maximum value
changes.

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