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# Parabola Graphs

 Overview & Parabolas Unit Overview. Parabola sketching & transformations Translation of the turning point y = ±a(x ± c)2 ± d Sketching factorised parabolas y = ±a(x ± b)(x ± c) Going from a graph to/from an equation Remember to define the Domain if you write the equation for part of a parabola graph. Parabola Transformations (Allow macros on spreadsheets) Ex10.01, Ex10.02 p41, p42

# Basic parabola

Square each x value to get y

Remember a negative squares to give a positive

(mouse-over to see the graph change)

x y
3 9
2 4
1 1
0 0
-1 1
-2 4
-3 9

# Inverted parabola

 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 parabola graph Mouse-over the equations to see the graph translation

# Horizontal shift

 Adding a constant to x horizontally translates the parabola 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)

 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