1. Completing the square
means writing the unknown terms of a quadratic in a square bracket
Example
because
Application
To find the maximum or minimum value of this function.
has a minimum value
when x = – 3
Minimum value of
is – 2
Minimum point on the curve
is (– 3 , – 2)

2. Example
To sketch the graph of
line of symmetry y x
has a minimum value
when x = 1 5
Minimum point is (1, 3)
(1, 3)
Intercept on the y axis
is 5
x = 1

3. (Note you can find the intercepts on the x axis by solving )
Example
To sketch the graph of y x
(–2, 7)
x = –2
has a maximum value
when x = – 2 3
Maximum point is (–2, 7)
Intercept on the y axis
is 3
(Note you can find the intercepts on the x axis by solving )