document.write( "Question 310097: 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 = ax2 + bx + c \n" ); document.write( "
Algebra.Com's Answer #221815 by ankor@dixie-net.com(22740)\"\" \"About 
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A company has sales (measured in millions of dollars) of 50, 60, and 75 during the first three consecutive years.
\n" ); document.write( " Find a quadratic function that fits these data, and use the result to predict the sales during the fourth year.
\n" ); document.write( " Assume that the quadratic function is of the form y = ax2 + bx + c
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of the year, we can develop 3 equations from this
\n" ); document.write( ":
\n" ); document.write( "Eq1: x=1, y=50
\n" ); document.write( "a(1^2) + 1b + c = 50
\n" ); document.write( "a + b + c = 50
\n" ); document.write( ":
\n" ); document.write( "Eq2: x=2, y=60
\n" ); document.write( "a(2^2) + 2b + c = 60
\n" ); document.write( "4a + 2b + c = 60
\n" ); document.write( ":
\n" ); document.write( "Eq3: x=3, y=75
\n" ); document.write( "a(3^2) + 3b + c = 75
\n" ); document.write( "9a + 3b + c = 75
\n" ); document.write( ":
\n" ); document.write( "Subtract eq1 from eq2
\n" ); document.write( "4a + 2b + c = 60
\n" ); document.write( "a + b + c = 50
\n" ); document.write( "--------------------Eliminates c
\n" ); document.write( "3a + b = 10
\n" ); document.write( ":
\n" ); document.write( "Subtract eq2 from eq3
\n" ); document.write( "9a + 3b + c = 75
\n" ); document.write( "4a + 2b + c = 60
\n" ); document.write( "---------------------eliminates c again
\n" ); document.write( "5a + b = 15
\n" ); document.write( ":
\n" ); document.write( "Using these two 2 unknown equation to eliminate b
\n" ); document.write( "5a + b = 15
\n" ); document.write( "3a + b = 10
\n" ); document.write( "----------------Subtraction eliminates b, find a
\n" ); document.write( "2a = 5
\n" ); document.write( "a = 2.5
\n" ); document.write( ":
\n" ); document.write( "Use the eq: 5a + b = 15, to find b
\n" ); document.write( "5(2.5) + b = 15
\n" ); document.write( "12.5 + b = 15
\n" ); document.write( "b = 15 - 12.5
\n" ); document.write( "b = 2.5
\n" ); document.write( ":
\n" ); document.write( "Use eq1 to find c
\n" ); document.write( "2.5 + 2.5 + c = 50
\n" ); document.write( "5 + c = 50
\n" ); document.write( "c = 50 - 5
\n" ); document.write( "c = 45
\n" ); document.write( ":
\n" ); document.write( "The equation: y = 2.5x^2 + 2.5x + 45
\n" ); document.write( ":
\n" ); document.write( "\"use the result to predict the sales during the fourth year.\"
\n" ); document.write( "x = 4
\n" ); document.write( "y = 2.5(4^2) + 2.5(4) + 45
\n" ); document.write( "y = 2.5(16) + 10 + 45
\n" ); document.write( "y = 40 + 10 + 45
\n" ); document.write( "y = 95 million in the 4th year
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\n" ); document.write( "How about this? Did it make sense to you???\r
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