(2.2) Quadratic Functions
•Graphing Quadratic Functions
•Finding x-intercepts
•Finding Maximum or Minimum values
Vertex Form of a Quadratic Function
f ( x) = a ( x − h) + k
2
Vertex :
( h, k )
Vertex and Intercept Forms of
a Quadratic Function
ax + bx + c Form f ( x ) = ax + bx + c
2
2
 b
Vertex :  −
,
 2a
 b 
f −

 2a  
Graphing Quadratic Functions with
Equations in Vertex Form
1. f ( x ) =
− ( x + 1) + 2
2
Graphing Quadratic Functions
in Other Forms
2. f ( x ) =
− x2 − 4 x + 1
Domain of f =
Range of f =
Graphing Quadratic Functions with
Equations in Standard
Form
2
3. =
f ( x) 2( x) − 3
Domain of f =
Range of f =
Graphing Quadratic Functions
in Other Forms
4. f ( x ) = x 2 + 2 x + 1
Domain of f =
Range of f =
( −∞, ∞ )
Modeling Quadratics
5. s ( t ) =
−10t + 40t + 150
a. Find the maximum (vertex)
2
Modeling Quadratics
5. s ( t ) =
−10t + 40t + 150
b. Find the time when the height ( s(t )) is 0
2
Modeling Quadratics
5. s ( t ) =
−10t + 40t + 150
c. Find s ( 0 ) and describe what it means.
2
Modeling Quadratics
5. s ( t ) =
−10t + 40t + 150
d . Graph the function.
2
s(t)
200
160
120
80
40
t
1
2
3
4
5
6
7
Modeling Quadratics
6.
You have 120 feet of fencing to enclose a rectangular
region. Find the dimensions of the rectangle that
maximize the enclosed area. What is the maximum area?
y
x