Potw solution

John Hinsley’s PoTW Solution

Suppose that F(x+3)= 3x2+7x+4 and F(x)= ax2+bx+c. What is a+b+c?First, you take the equation F(x)= ax2+bx+c and substitute (x+3) forx.F(x)= ax2+bx+cF(x+3)= a(x+3)2 + b(x+3) + cF(x+3)= a(x2+6x+9) + bx + 3b + cF(x+3)= ax2 + 6ax + 9a + bx + 3b + cF(x+3)= ax2 + (6a+b)x + 9a + 3b + c

In the equation F(x+3)= 3x2+7x+4, 3 is the a term, 7 is the b term, and 4 is the c term. In the equation F(x+3)= ax2 + (6a+b)x + 9a + 3b + c, a is the a term, (6a+b) is the b term, and 9a is the c term.If you set the terms equal to each other, you geta=3, 7= 6a+b, and 4= 9a + 3b + c.Now you have a system of two variables with7= 6a+b and 4= 9a + 3b + c.

Solve:7= 6a + b4= 9a + 3b + c7= 6a + b 4= 9a + 3b + c7= 6(3)+ b 4= 9(3) + 3(-11) + c7= 18 + b 4= 27 - 33 + c-11= b 4= -6 + c 10= ca+b+c=3-11+10=2 a+b+c=2

Potw solution

by jwhinsley on Apr 13, 2011

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