Intermediate Algebra (11th edition)

Using the General Characteristics to Graph a Parabola

Graph

The parabola opens down (because ) and is narrower than the graph of

since This causes values of to decrease more

quickly than those of This parabola has vertex as shown in

FIGURE 10. To complete the graph, we plotted the ordered pairs and, by sym-

metry, Symmetry can be used to find additional ordered pairs that satisfy

the equation.

1 - 2, 2 2.

1 - 4, 2 2

ƒ 1 x 2 =-x^2. 1 - 3, 4 2 ,

ƒ 1 x 2 =x^2 , |- 2 |=2 and 2 7 1. F 1 x 2

a 6 0

F 1 x 2 =- 21 x+ 322 + 4.

EXAMPLE 5

SECTION 9.5 Graphs of Quadratic Functions 535

NOW TRY

x

y

–3^0

2

4

F(x) = –2(x + 3)^2 + 4

x = –3

FIGURE 10

Vertex:

Axis:

Domain:

Range: 1 - q, 4 4

1 - q, q 2

x=- 3

1 - 3, 4 2

F 1 x 2 =- 21 x+ 322 + 4

OBJECTIVE 4 Find a quadratic function to model data.

Modeling the Number of Multiple Births

The number of higher-order multiple births (triplets or more) in the United States has

declined in recent years, as shown by the data in the table. Here, xrepresents the number

of years since 1995 and yrepresents the number of higher-order multiple births.

EXAMPLE 6

Source:National Center

for Health Statistics.

Year x y

1995 0 4973

1996 1 5939

1997 2 6737

1999 4 7321

2001 6 7471

2003 8 7663

2004 9 7275

2005 10 6694

Find a quadratic function that models the data.

A scatter diagram of the ordered pairs is shown in FIGURE 11on the next

page. The general shape suggested by the scatter diagram indicates that a parabola

should approximate these points, as shown by the dashed curve in FIGURE 12. The

equation for such a parabola would have a negative coefficient for since the

graph opens down.

x^2

1 x, y 2

NOW TRY

EXERCISE 5

Graph .ƒ 1 x 2 = 21 x- 122 + 2

NOW TRY ANSWER
5.

01 x

y

2

f(x) = 2(x – 1)^2 + 2