f (x) = x 2 - 2x - 8
AOS:
Vertex:
f (x) £ x 2 - 2x - 8
f (x) ³ x 2 - 2x - 8
0  x2  2 x  8
0 ³ x 2 - 2x - 8
test point: (0,0)
test point: (0,0)
f (x) < x 2 - 2x - 8
f (x) > x 2 - 2x - 8
0 < x 2 - 2x - 8
0 > x 2 - 2x - 8
test point: (0,0)
test point: (0,0)
Inequality
f ( x)  x 2  2 x  8
f ( x)  x 2  2 x  8
f ( x)  x 2  2 x  8
f ( x)  x 2  2 x  8
y
y
y
y
5
5
Graphical
Solution
5
5
x
x
-8
-6
-4
-2
2
4
6
x
x
-8
8
-6
-4
-2
2
4
6
8
-8
-6
-4
-2
2
4
6
-8
-6
-4
-2
2
4
6
8
8
-5
-5
-5
Solution as
Interval
Notation
Solutions can’t be given in interval notation. They are the entire shaded regions on the
graph.
0  x2  2 x  8
Inequality
Graphical
Solution
-5
0  x2  2 x  8
















0  x2  2 x  8
0  x2  2 x  8


-2

-2
4

4






-2










-2
4
4
Solution as
Interval
Notation
(, 2)  (4, )
( 2, 4)
(, 2]  [4, )
[2, 4]
Inequality
f ( x)  x 2  2 x  8
f ( x)  x 2  2 x  8
f ( x)  x 2  2 x  8
f ( x)  x 2  2 x  8
y
y
y
y
5
5
Graphical
Solution
5
5
x
x
-8
-6
-4
-2
2
4
6
8
x
x
-8
-6
-4
-2
2
4
6
8
-8
-6
-4
-2
2
4
6
-8
-6
-4
-2
2
4
6
8
8
-5
-5
-5
Solution as
Interval
Notation
Solutions can’t be given in interval notation. They are the entire shaded regions on the
graph.
0  x2  2 x  8
Inequality
Graphical
Solution
Solution as
Interval
Notation
-5
0  x2  2 x  8



-2













0  x2  2 x  8
0  x2  2 x  8


4
(, 2)  (4, )

-2
4
( 2, 4)



-2





4
(, 2]  [4, )









-2
4
[2, 4]
A business offers tours to San Antonio. The profit P that the company earns for x number of tourists
can be modeled by P( x)  2.5x 2  100 x  300 . How many people are needed for a profit of at least
$500?
A football thrown by a quarterback follows a path given by h( x)  0.0095x 2  x  7 , where h is the
height of the ball in feet and x is the horizontal distance the ball has traveled in feet. If any height less
than 10 feet can be caught or knocked down, at what distances from the quarterback can the ball be
knocked down?
A business offers tours to San Antonio. The profit P that the company earns for x number of tourists
can be modeled by P( x)  2.5x 2  100 x  300 . How many people are needed for a profit of at least
$500?
A football thrown by a quarterback follows a path given by h( x)  0.0095x 2  x  7 , where h is the
height of the ball in feet and x is the horizontal distance the ball has traveled in feet. If any height less
than 10 feet can be caught or knocked down, at what distances from the quarterback can the ball be
knocked down?