Question

A company's yearly profits from 1996 to 2006 can be modeled by the function y=x^2-10x+125 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?

Answer 1

year 0 = 1996, year 10 = 2006. plot y=x^2-10x+125 for values of x from 0 to 10. find the value of x at the bottom of the parabola, add 1996 to give you the year in which it had the lowest profit. plug in that value of x to find that year's profit (remember to multiply by $1,000 as the formula gives you the answer in thousands of dollars)

if you know calculus, you can figure out the inflection point by taking the first derivative with respect to x and setting it to 0 (the slope will be zero at the point where it changes from going up to down or vice versa). dy/dx = 2x - 10 = 0. x = ?