Question

A company's yearly profits from 1996 to 2006 can be modeled by a function y = x2 - 8x + 80, where y is the profit and x is the number of years since 1996. what was the company's least yearly proft during the time period?

Answer 1

The least yearly profit during 1996 to 2006 was in year 2000 and was 64, calculated using the vertex of the quadratic function y = x^2 - 8x + 80.

Step-by-step explanation:

The company's least yearly profit during the time period from 1996 to 2006 can be found by determining the minimum value of the quadratic function y = x2 - 8x + 80, where y represents the profit and x is the number of years since 1996. To find the minimum value, we can use the vertex formula for a quadratic function, which is -b/2a. In our function, the coefficients are a = 1 and b = -8.

To find the vertex: x = -(-8)/(2*1) = 8/2 = 4. This means that the least profit occurred 4 years after 1996, which is 2000. Substituting x = 4 back into the function: y = (4)2 - 8(4) + 80 = 16 - 32 + 80 = 64. Therefore, the least yearly profit was 64.