# AS 2.2 Graphs Revision

 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 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 #### 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)

## 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)

#### back to top 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

# 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

c

## 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)

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

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

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

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