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

1. Use any method to determine 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.

   Help (a):

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

   More Help 1(a):

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

   More Help 2(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. What is $f(x) + g(x)?$

   Hint (b):

   Substitute:

   $(x^2 - 2x + 6) + (2x + 11)$

   Answer (b):

   Simplify:

   $x^2 + 17$

3. What is $f(x) - g(x)?$

   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.