Chapter 9.2, Problem 47E

To determine

To graph the function.

Answer to Problem 47E

The solution is -0.2 and -5.9

Explanation of Solution

Given information:

  $f(x)=x^2+6x+1$

Graph:

  

Calculation:

The given equation is $f(x)=x^2+6x+1$

There are two intercepts: the one between 0 and -1, the 2^nd between -6 and -5.

Make a table between x - values between 0 and -1, -6 and -5. Use an increment of 0.1. Look for change of sign of the function values.

The table is

$x$	-5.1	-5.2	-5.3	-5.4	-5.5	-5.6	-5.7	-5.8	-5.9
$f(x)$	-3.59	-3.16	-2.17	-2.24	-1.75	-1.24	-0.71	-0.16	0.41

The change in sign is from -5.9.

$x$	-0.1	-0.2	-0.3	-0.4	-0.5	-0.6	-0.7	-0.8	-0.9
$f(x)$	0.41	-0.16	-0.71	-1.24	-1.75	-2.24	-2.71	-3.16	-3.59

The change in sign is from -0.2.

The function value that are closest to 0 correspond to x -values that best approximate the zeros of the function.

The closest value is -0.2 and -5.9.