Consider $f(x)=x^2−2x+6$ and $g(x)=2x+11$.  

1. Use any method to find the points of intersection of $f(x)$ and $g(x)$.

   Hint (a):

   One method is to graph $f(x)$ and $g(x)$ on the same set of axes and locate the point of intersection.

   More Help 1(a):

   To graph $f(x)$, make a table. You will need to use $x$-values from $x=−2$ to $x=5$.

   More Help 2(a):

   To use the equations, set $f(x)=g(x)$ and solve the resulting quadratic equation.

   More Help 3(a):

   Another method would be to make a table of values for each function and compare table values to find matches.

   Answer (a):

   Two points of intersection: $(−1,9)$ and $(5,21)$.

2. Calculate $f(x)+g(x)$.

   Hint (b):

   Substitute:
   $(x^2−2x+6)+(2x+11)$

   Answer (b):

   Simplify:
   $x^2+17$

3. Calculate $f(x)−g(x)$.

   Hint (c):

   How is this different from $f(x)+g(x)$?

   More Help (c):

   Remember to put parentheses around $2x+11$ and use the Distributive Property correctly.