Question in description

Question

A company’s yearly profits from 1996 to 2006 can be modeled by the function y=x^2-8x+80 where y is the profit (in thousands of dollars) and x is the number of years since 1996.

a) In what year did the company experience its lowest yearly profit?

b) What was the lowest yearly profit?

PLEASE HELLPPP!!

Answer 1

Hi there, Im Hriday, while this problem may seem complicated at first glance, it is simple once you break it down. The graph showing yearly profit is a parabola, meaning it looks like a U shape. if you graph this curve you will find this to be the case. considering the year 1996 as zero and the year 2006 as 10 we obtain a parabola opening upward. It looks like an uppercase U letter. because it opens upward the minimum point it either at 1996 or at the vertex of the graph. if the vertex of the graph is between 0 and 10, we can say the minimum point is at the vertex, if not the minimum must be at 1996. to find the vertex of the graph we use the simple mathematical formula -b/(2*a) while this formula may seem complicated, your parabloa should give you the related values, ax^2 +bx +c for this specific case is x^2 -8x +80. The values here are 1, -8 and 80. therefore your vertex is (-(-8))/(2*(2)) = 4 given that the starting year that we denoted as 1996 is zero, we can say that the answer to part (a) is 1996 +4 = 2000 for part (b) we simply need to "plug" the 4 from the previous answer4 back in to our equation to get a value for sales if we do this we should get 4^2 -8*4 + 80 = 64 thousand dollars. If you need any additional information please feel free to contact me through wyzant, my username is Hriday.trivedi