Question

Shivani launched her new company in the year 2000. Her company makes a yearly profit in lakhs as a quadratic function, P ( x ) , for the first 10 years since the launch, where x is the number of years since 2000 (i.e., x = 0 denotes the year 2000, x = 1 denotes the year 2001, and so on). Let the loss be represented as the negative of profit. In the year 2005 and 2008 the company had made neither profit nor loss, and in the year 2009 the company made some profit. Which of the following options are correct? >From the given information, the profit made by the company in the year 2010 is exactly ₹8 lakhs. > In the first ten years, the company made a loss in the years 2006 and 2007 only. >In the first ten years, the company made a loss in the year 2006 only. >In the first ten years, the company never made a loss. >From the given information, the profit made by the company in the year 2010 can not be determined. >From the given information, the loss made by the company in any year except 2004 and 2007 is more than 5 lakhs. >From the given information, the years for which the company made losses cannot be determined.​

Answer 1

Given :  company makes a yearly profit in lakhs as a quadratic function, P ( x ) , for the first 10 years since the launch, where x is the number of years since 2000 (i.e., x = 0 denotes the year 2000, x = 1 denotes the year 2001, and so on). Let the loss be represented as the negative of profit. In the year 2005 and 2008 the company had made neither profit nor loss, and in the year 2009 the company made some profit.

To Find : Correct Statement

Solution:

for the year 2005 and 2008  company made no loss no profit

Hence the quadratic function intersect x axis at 5 and 8

as 5 and 8 represents year 2005 and 2008 respectively

now in 2009 company made some profit

hence graph increased from 8 to 9

so  between 5 and 8 graph was in negative

so loss was in year 2006 and 2007

Hence , In the first ten years, the company made a loss in the years 2006 and 2007 only.

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