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EXAMPLE 3

FILM PRODUCTION. For the period 1971  2001 , the number y of films produced in the world can be modeled by the function y = 10 x 2  94 x + 3900 where x is the number of years since 1971 . In what year were 4200 films produced ?. EXAMPLE 3.

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EXAMPLE 3

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  1. FILM PRODUCTION For the period 1971  2001, the number y of films produced in the world can be modeled by the functiony = 10x2  94x + 3900 wherexis the number of years since1971. In what year were 4200 films produced? EXAMPLE 3 Use the quadratic formula SOLUTION y =10x2– 94x+ 3900 Write function. 4200 = 10x2– 94x – 3900 Substitute 4200 for y. 0 = 10x2– 94x – 300 Write in standard form.

  2. (–94)2 – 4 (10)(–300) + –(–94) x = – 2(10) 20,836 94 = 20 20,836 94 – 20,836 94+ 12 –3. and 20 20 + There were 4200 films produced about 12 years after 1971, or in 1983. – ANSWER EXAMPLE 3 Use the quadratic formula Substitute values in the quadraticformula: a =10,b = –94, andc =–300. Simplify. The solutions of the equation are:

  3. 1986 ANSWER for Example 4 GUIDED PRACTICE 4. WHAT IF? In Example 3, find the year when 4750 films were produced.

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