SOLUTION: Solve the problem. 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 da

Question 824501: Solve the problem.
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 = ax^2 + bx + c
Answers:
A) y = (15/2)^x2 - (25/2)x + (325/4); sales during the fourth year = $151.25 million
B) y = -5x^2 + 40x +15; sales during the fourth year = $95 million
C) y = (5/2)x^2 + (5/2)x + 45; sales during the fourth year = $95 million
D) y = 5x^2 + 5x + 40; sales during the fourth year = $180 million

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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the given data:
(1,50)
(2,60)
(3,75)
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plug given data into standard quadratic equation: y = ax^2 + bx + c
50 = a + b + c
60 = 4a + 2b + c
75 = 9a + 3b + c
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now we have a system of linear equations
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put the system of linear equations into standard form
---
50 = x + y + z
60 = 4x + 2y + z
75 = 9x + 3y + z
---
x + y + z = 50
4x + 2y + z = 60
9x + 3y + z = 75
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copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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x= 2.5
y= 2.5
z= 45
---
answer:
a= 2.5
b= 2.5
c= 45
the quadratic equation is: y = 2.5x^2 + 2.5x + 45
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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