A height of 206 ft means that so we substitute 206 for hin the
equation.
Let
Interchange sides.
Standard form
Divide by.
Factor.
Zero-factor propertyor Solve each equation.
Since we found two acceptable answers, the ball will be 206 ft
above the groundtwice, once on its way up and once on its way
down, at sec and at 10 sec. See FIGURE 4.
5
4t=
5
4
4 t= 5 t= 10
4 t- 5 = 0 or t- 10 = 0
14 t- 521 t- 102 = 0
4 t^2 - 45 t+ 50 = 0 - 4
- 16 t^2 + 180 t- 200 = 0
- 16 t^2 + 180 t+ 6 = 206
206 =- 16 t^2 + 180 t+ 6 h=206.
h=- 16 t^2 + 180 t+ 6
h=206,
404 CHAPTER 6 Factoring and Applications
206 f tFIGURE 4Modeling the Foreign-Born Population of the United StatesThe foreign-born population of the United States over the years 1930–2007 can be
modeled by the quadratic equation
where represents 1930, represents 1940, and so on, and yis the num-
ber of people in millions. (Source: U.S. Census Bureau.)
(a)Use the model to find the foreign-born population in 1980 to the nearest tenth of
a million.
Since represents 1930, represents 1980. Substitute 50 for xin the
equation.
Let.
Round to the nearest tenth.In 1980, the foreign-born population of the United States was about 14.6 million.
(b)Repeat part (a) for 2007.
For 2007, let.
Round to the nearest tenth.In 2007, the foreign-born population of the United States was about 36.0 million.
y=36.0
y=0.01048 17722 - 0.5400 1772 + 15.43 x= 77
y=14.6
y=0.01048 15022 - 0.5400 1502 + 15.43 x= 50
x= 0 x= 50
x= 0 x= 10
y=0.01048x^2 - 0.5400x+15.43,
EXAMPLE 5
Finding the Height of a BallA tennis player’s serve travels 180 ft per sec (123 mph). If she hits the ball directly
upward, the height hof the ball in feet at time tin seconds is modeled by the quad-
ratic equation
How long will it take for the ball to reach a height of 206 ft?
h=- 16 t^2 + 180 t+ 6.
NOW TRY EXAMPLE 4
EXERCISE 4
Refer to Example 4.How
long will it take for the ball
to reach a height of 50 ft?
NOW TRY ANSWER
4.^14 sec and 11 sec
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