document.write( "Question 1096703: Determine whether a quadratic model exists for the set of values below. If​ so, write the model.
\n" ); document.write( "f(0)=1, f(3)=-20,f(-1)=-4
\n" ); document.write( "Thank you, \n" ); document.write( "
Algebra.Com's Answer #711108 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
Determine whether a quadratic model exists for the set of values below. If​ so, write the model.
\n" ); document.write( "f(0)=1, f(3)=-20,f(-1)=-4
\n" ); document.write( "---------
\n" ); document.write( "The 3 points are not colinear --> quadratic.
\n" ); document.write( "----
\n" ); document.write( "y = ax^2 + bx + c
\n" ); document.write( "For (-1,-4)
\n" ); document.write( "-4 = a - b + c for (-1,-4)
\n" ); document.write( "1 = 0a + 0b + c for (0,1)
\n" ); document.write( "-20 = 9a + 3b + c for (3,-20)
\n" ); document.write( "----------
\n" ); document.write( "1 = 0a + 0b + c for (0,1) --> c = 1
\n" ); document.write( "---
\n" ); document.write( "a - b + 1 = -4
\n" ); document.write( "a - b = -5
\n" ); document.write( "---
\n" ); document.write( "9a + 3b + 1 = -20
\n" ); document.write( "9a + 3b = -21
\n" ); document.write( "3a + b = -7
\n" ); document.write( "a - b = -5
\n" ); document.write( "----------------- Add
\n" ); document.write( "4a = -12
\n" ); document.write( "a = -3
\n" ); document.write( "-----
\n" ); document.write( "b = 2
\n" ); document.write( "f(x) = -3x^2 + 2x + 1\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );