Choose the one alternative that best completes the statement or answers the question.
-A company has sales (measured in millions of dollars) of 50,60 , and 75 during the first three consecutive years. Find a quadratic function that fits these data, and use the result to predict the sales during the fourth year.
Assume that the quadratic function is of the form $y = a x ^ { 2 } + b x + c$
A) $y = \frac { 5 } { 2 } x ^ { 2 } + \frac { 5 } { 2 } x + 45$; sales during the fourth year $= \$ 95$ million
B) $y = - 5 x ^ { 2 } + 40 x + 15$; sales during the fourth year $= \$ 95$ million
C) $y = 5 x ^ { 2 } + 5 x + 40$; sales during the fourth year $= \$ 180$ million
D) $y = \frac { 15 } { 2 } x ^ { 2 } - \frac { 25 } { 2 } x + \frac { 325 } { 4 } ;$ sales during the fourth year $= \$ 151.25$ million

Question

Quizplus · Accepted Answer

To find a quadratic function that fits the given data, we substitute the sales figures into the quadratic equation $y = ax^2 + bx + c$ for the years $x = 1, 2, 3$, resulting in a system of equations. Solving this system yields the coefficients $a = \frac{5}{2}$, $b = \frac{5}{2}$, and $c = 45$. Using this equation to predict the sales for the fourth year ($x = 4$) gives us $95$ million dollars.

Choose the One Alternative That Best Completes the Statement or Answers