Find a power function that models the data in the table. Round to three decimal places if necessary.
-The following points form a quadratic relationship: (1, 5.0), (2, 4.4), (3, 4.3), (4, 4.2), (5, 4.6), (6, 4.8), (7, 5.4), (8, 6.2) . The x-coordinates are the years a particular company has been in operation and the y-coordinates are the
Profit, in millions, for that year. Find the quadratic function that models the profit in millions as a function of x,
The number of years of operation. Round to three decimal places.
A) $y = 0.099 x ^ { 2 } + 1.254 x - 3.512$
B) $y = 0.101 x ^ { 2 } - 0.723 x + 5.552$
C) $y = 0.203 x ^ { 2 } - 0.945 x + 7.098$
D) $y = - 0.003 x ^ { 2 } + 0.145 x - 0.892$

Question

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The following points form a quadratic relationship: (1, 5.0), (2, 4.4), (3, 4.3), (4, 4.2), (5, 4.6), (6, 4.8), (7, 5.4), (8, 6.2) . The x-coordinates are the years a particular company has been in operation and the y-coordinates are the
Profit, in millions, for that year. Find the quadratic function that models the profit in millions as a function of x,
The number of years of operation. Round to three decimal places. 
A) $y = 0.099 x ^ { 2 } + 1.254 x - 3.512$
B) $y = 0.101 x ^ { 2 } - 0.723 x + 5.552$
C) $y = 0.203 x ^ { 2 } - 0.945 x + 7.098$
D) $y = - 0.003 x ^ { 2 } + 0.145 x - 0.892$

Quizplus · Accepted Answer

To find the correct quadratic function that models the given data, one would typically use regression analysis or a system of equations derived from plugging in the given points into the general form of a quadratic equation, $y = ax^2 + bx + c$. Without performing these calculations directly here, choice B is identified as correct because it is the only option that seems to fit the general trend of the data points provided, which initially decrease, reach a minimum, and then increase. The coefficients in option B suggest a shape that would match this pattern, with a positive $a$ (indicating the parabola opens upwards) and values of $b$ and $c$ that would adjust the vertex and intercept to fit the given points.

Find a Power Function That Models the Data in the Table