FUNCTIONS SUMMARY

Functions Summary
The Basic Graphs and the Effect of Parameters

The Straight Line

y x y ax  p
‘a’ changes the gradient of the graph; p shifts the graph up or down and is the y intercept
The Parabola:

y x 2
y ax 2 ' a 'stretches the graph a  0min value a  0max value
2
y ax  q q shifts the graph up (q  0)or down ( q  0)by q units TP = y int = (0 ;q )
2
y ax  bx  c Standard Form with y cut c
y a ( x  p )2  q Turning Point FormT P ( p; q ) The graph of y x 2 has shifted p units to theleft or right
y ( x  2)2 shifts y x 2 2 units to the right and y ( x  2) 2 shifts y x 2 2 units to the left
y a ( x  x1 )( x  x2 ) Factorised Form with x cuts x1 and x2
Domain : x  Range: , y minum value or y maximum vlaue
b (x  x )
Axis of symmetry: x  or x  p if y a( x  p) 2  q or x  1 2 if x intercepts are given
2a 2




The Hyperbola

1
y
x
a
y a moves hyperbola away from the point closest to the origin
x
If a  0 hyperbola lies in Quads1 and 3 If a  0,hyperbola lies in quads 2 and 4
x 0 and y  0 are the horizontal and vertical asymptotes
a a
y  q y q is the vertical asymptote (hyperbola y  has moved up q units)
x p x
x  p is the horizontal asymptote
Domain : x  R x  p Range : y , y q
Axes of symmetry:
a
y x and y  x for y 
x
a
y ( x  p)  q and y  ( x  p )  q for y  q
x p