  ### Home > INT3 > Chapter 1 > Lesson 1.2.2 > Problem1-80

1-80.

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 $g(x)$.

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. What is $f(x) + g(x)?$

Substitute:

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

Simplify:

$x^2 + 17$

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

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: Int3 1-80 HW eTool