Chapter 1.4, Problem 20E

To determine

Find the intersection points.

Answer to Problem 20E

  $\boxed{\text{ x}=-\text{3 and x}=-\text{4}}$

Explanation of Solution

Given information:

Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there?

  $y=6-4x-x^2,y=3x+18;[-6,2]$ by $[-5,20]$

Calculation:

  

From this graph, one can see that there are two points of intersection in the given viewing window. To check this, we set the fuctions equal to one another and solve:

  $\begin{array}{l}6-4x-x^2=3x+18\\ 0=12+7x+x^2\text{ which factors into}:\end{array}$

  $0=(x+3)(x+4) \text{which gives the unique solutions x}=-\text{3 and x}=-\text{4}$ .

Hence, we conclude that there are two points of intersection, $\boxed{\text{ x}=-\text{3 and x}=-\text{4}}$.