Cambridge Additional Mathematics

GRAPHING

PACKAGE

Quadratics (Chapter 3) 77

Discovery 2 Graphing y=a(x¡h)^2 +k

This Discovery is also best done using technology.

What to do:

1aUse technology to help you to sketch:

y=(x¡3)^2 +2, y=2(x¡3)^2 +2, y=¡2(x¡3)^2 +2,

b Find the coordinates of the vertex for each function ina.

c What is the geometrical significance ofain y=a(x¡3)^2 +2?

2aUse technology to help you to sketch:

y=2(x¡1)^2 +3, y=2(x¡2)^2 +4, y=2(x¡3)^2 +1,

b Find the coordinates of the vertex for each function ina.

c What is the geometrical significance ofhandkin y=2(x¡h)^2 +k?

3 Copy and complete:

If a quadratic has the form y=a(x¡h)^2 +k then its vertex has coordinates ......

The graph of y=a(x¡h)^2 +k is a ...... of the graph of y=ax^2 with vector ......

Quadratic form, a 6 =0 Graph Facts

² y=a(x¡p)(x¡q)

p,qare real

x-intercepts arepandq

axis of symmetry is x=

p+q

2

vertex is

³p+q

2

,f

³p+q

2

́ ́

² y=a(x¡h)^2

his real

touchesx-axis ath

axis of symmetry is x=h

vertex is(h,0)

² y=a(x¡h)^2 +k axis of symmetry is x=h

vertex is(h,k)

x=h

V,(h k)

x=h

V,(h 0) x

p q x

p+q

x = ^^^^

2____________

y=¡(x¡3)^2 +2, and y=¡^13 (x¡3)^2 +2

y=2(x+1)^2 +4, y=2(x+2)^2 ¡ 5 , and y=2(x+3)^2 ¡ 2

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_03\077CamAdd_03.cdr Thursday, 3 April 2014 4:25:13 PM BRIAN