### Home > A2C > Chapter 1 > Lesson 1.2.1 > Problem1-71

1-71.

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 $g(x)$.

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

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

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

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

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

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

Substitute:

$(x^2−2x+6)+(2x+11)$

Simplify:

$x^2+17$

3. Calculate $f(x)−g(x)$.

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

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

Use the blank graph in the eTool below to solve the problem.
Click the link at right for the full version of the eTool:  1-71 HW eTool