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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos

AS 2.2 Graphs Revision

Graphs HOME | Achievement Objectives | Parabola Graphs | Parabola Questions | Cubics | Hyperbola | Circles | Exponential | Logs | Radians | Trig Graphs Overview | Trig Vertical Shift | Trig Horizontal Shift | Trig Equations | Trig Models | General Translations | Applications | Revision

26



Excellence questions

Yay

Harder revision Questions | Answers A | B

 

Class notes, Blank notes

Excellence Starters | blank version

Log and exponential applications Ex13.05

p49, p50

27



Revisionfor Achievement Standard 2.2 Graphs

Remember to define the Domain if you write the equation for part of ANY graph.

Revision Page, Link to previous Exam Papers

Revision tests and worked answers

Graphing Starters | web version (firefox may have issues -try IE)

NZQA annotated exemplars A and B and the assessments on TKI

 

Mixed Graphs | Answers | Daves Revision | Another revision sheet

pg158

Revision | Exam Papers

p55, p56, p57, p58

web links

 

Jump down to... Parabolas | Cubics | Hyperbolas | Circles | Exponential | Log

Links to Exemplars on TKI 2.2 A (Word, 156 KB) | 2.2 B (Word, 155 KB) | 2.2 C (Word, 1 MB)

 

 

Parabola

http://www.waldomaths.com/Functions1N.jsp

Mixed Graphing Starter Questions | Link to Exam Papers

Parabolas
y = x2

 

Vertical Shift
Horizontal Shift
Horizontal & Vertical Shift
y = x2 - 3
y = (x + 1)2
y = (x + 2)2 - 4
p
Vertical Stretch
Factorised Parabola
Inverted Parabola
y = 3x2
y = (x + 1)(x - 2)
y = -x(x - 3)
or y = x(3 - x)

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Sketch y = (x - 3)(x + 1)
Mark the x intercepts
Make each bracket = 0

y = (x - 3)(x + 1)
How do we make (x - 3) = 0? put x = 3
How do we make (x + 1) = 0? put x = -1
y = (x - 3)(x + 1)
x = 3 or x = -1
The graph is symmetrical about a midline
Midline at x = 1
Distance to midline squared is distance vertically to turning point
Across 2 so down 22 = 4
Sketch graph symmetrically
Check y intercept (put x = 0 in equation)
y = (x - 3)(x + 1)
y = (0 - 3)(0 + 1)
y = (- 3)(1)
y = -3

y intercpt at -3

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Level 2 Problem

Find the equation of the graph y = ?
Use the turning point to get the horizontal & vertical shift

Side shift to 4
so we have y = (x - 4)2  

Vertical shift to 5

so we have y = x2 + 5

Combined we get
y = (x - 4)2 + 5
y = (x - 4)2 + 5
Use the known point (0,3) to find the vertical stretch

Negative because inverted graph
y = -?(x - 4)2 + 5
We go across 4 so we should go down 42 = 16

However we only go down by 2 so the stretch is 2/16 or  1/8
y = -1/8 (x - 4)2 + 5
Equation:
y = -1/8 (x - 4)2 + 5 
 

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c

Cubics y = x3

y=x(x+2)(x-2)

 

Vertical Shift
Horizontal Shift
Horizontal & Vertical Shift
y = x3 - 2
y = (x - 3)3
y = (x + 3)3 + 2
p
Vertical Stretch
Inverted Cubic
Factorised Cubic
y = 0.25x3
y = -x3
y=(x+1)(x+2)(x-1)
p
Factorised Cubic
Factorised Cubic
Stretched Cubic
y = x(x + 3)2
y = x2(x - 2)
y=2(x+1)(x+2)(x-1)

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h

Hyperbolas
y = 2/x

 

Vertical Shift
Horizontal Shift
Horizontal & Vertical Shift
y = 2/x + 3
y = 3/(x+1)
y = 2/(x+2) - 1
p
Inverted Hyperbola
Hyperbola Family
Fraction
y = -2/(x-2)
y = 2/x or 4/x or 6/x
y = 7/2x

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c

Circles
x2 + y2 = r2

 

Vertical Shift
Horizontal Shift
x2 + (y - 2)2 = 9
(x - 2)2 + y2 = 9
p
Horizontal & Vertical Shift
Changing radius
(x-2)2 + (y+3)2 = 4
x2 + (y - 2)2 = 9 or 4

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e

Exponential
y = 2x

 

Changing the base
Changing the base
Reflect in y axis
y = 2x y = 2x
y = 2x y = 0.5x
y = 2x y = 2-x
p
Vertical Shift
Horizontal Shift
Horizontal & Vertical Shift
y = 2x - 3
y = 2x - 3
y = 3 x - 3 - 2

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e

Logarithmic
y = Log2x

 

Changing the base
Reflect in x axis
Reflect in y axis
y = Log2x
y = Log4x
y = Log8x
y = -Log2x
y = Log2-x
p
Vertical Shift
Horizontal Shift
Horizontal & Vertical Shift
y = Log2x - 3
y = Log2(x - 2)
y = Log2(x + 2) + 3

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