Use a system of linear equations to find the quadratic function f(x)=ax2+bx+c that satisfies the given conditions. Solve the system using matrices. f(1)=−1, f(2)=−2, f(3)=−7 f(x)=?

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Use a system of linear equations to find the quadratic function  f(x)=ax2+bx+c  that satisfies the given conditions. Solve the system using matrices.  f(1)=−1, f(2)=−2, f(3)=−7  f(x)=?

navratitehf · Accepted Answer

Step 1  By using the given information,  Solving the quadratic equation for x=1  f(1)=a(1)2+b×1+c  −1=a+b+c  Solving the quadratic equation for x=2,  f(2)=a(2)2+b×2+c  −2=4a+2b+c  Solving the quadratic equation for x=3,  f(3)=a(3)2+b×3+c  −7=9a+3b+c  Step 2  Solving the equations to get the value of a, b and c,  i) a=−1−b−c  −2=4(−1−b−b)+2b+c  −2=−4−b−4c+2b+c  2=−2b−3c  ii) c=−(2b+23)  Substituting the value of  in equation (i) then,  a=−1−b−(−2b+23)  a=−3−3b+2b+23  a=−1−b3  Step 3  Substituting the value of a and c in expression of x=3 then,  9a+3b+c=−7  9(−1−b3)+3b−(2b+23)=−7  −9−9b+9b−2b−2=−21  −2b=−10  b=5  Then the value of a and c is,  a=−2, c=−4  Hence the quadratic equation is,  f(x)=−2x2+5x−4

Use a system of linear equations to find the quadratic

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