# Cubic Graphs

 Cubic Functions & Graphs Basic Cubic graph y = x3, Translated Cubic using the turning point y = ±a(x ± c)2 ± d Sketching factorised cubics y = ±a(x ± b)(x ± c)(x ± d) and other forms eg. y = ±a(x ± b)(x ± c)2 Remember to define the Domain if you write the equation for part of a cubic graph. Cubic Graphs (Allow macros on spreadsheets)  Ex10.04 Cubics p44, GeoGebra Java Cubics | With Brackets

# Basiccubic

Cubic rule x y
3 27
2 8
1 1
0 0
-1 -1
-2 -8
-3 -27 # Inverted cubic

 A negative multiplier inverts the graph about the turning point     Mouse-over the equations to see the graph translation    # Vertical shift

 Adding a constant vertically translates the cubic graph Mouse-over the equations to see the graph translation     # Horizontal shift

 Adding a constant to x horizontally translates the cubic graph Mouse-over the equations to see the graph translation     # Combined shifts

 Horizontal and vertical shifts can be combined Mouse-over the equations to see the graph translation    ### Note: Translate the turning point (0,0), then sketch the graph from this point

Excel demo (contains macros)

# Factored cubics

 Find the x intercepts by making each bracket = 0   Find the y intercept by putting x = 0 in the equation   Mouse-over the equations to see the graph translation    # Vertical stretch

 A multiplier stretches or compresses the graph vertically   Mouse-over the equations to see the graph translation     