Chapter 9.8, Problem 33STP

(a)

To determine

To calculate: To graph function

Answer to Problem 33STP

Graph of function is plotted

Explanation of Solution

Given information: Function is $y=\frac{1}{2}{x}^2+3$

Calculation:

Function is given as

  $y=\frac{1}{2}{x}^2+3$

When $x=0$

  $y=\frac{1}{2}{\left(0\right)}^2+3=0+3=3$

When $x=1$

  $y=\frac{1}{2}{\left(1\right)}^2+3=\frac{1}{2}+3=\frac{7}{2}$

When $x=-1$

  $y=\frac{1}{2}{\left(-1\right)}^2+3=\frac{1}{2}+3=\frac{7}{2}$

When $x=2$

  $y=\frac{1}{2}{\left(2\right)}^2+3=2+3=5$

When $x=-2$

  $y=\frac{1}{2}{\left(-2\right)}^2+3=2+3=5$

When $x=3$

  $y=\frac{1}{2}{\left(3\right)}^2+3=\frac{9}{2}+3=\frac{15}{2}$

When $x=-3$

  $y=\frac{1}{2}{\left(-3\right)}^2+3=\frac{9}{2}+3=\frac{15}{2}$

Function table is

x	y
-3	$\frac{15}{2}$
-2	5
1	$\frac{7}{2}$ -5
0	3
1	$\frac{7}{2}$ -5
2	5
3	$\frac{15}{2}$

Plotting the points on graph:

  

Conclusion:

Hence, graph of function is plotted

(b)

To determine

To calculate: To find the minimum value of function

Answer to Problem 33STP

Minimum value of function is $3$

Explanation of Solution

Given information: Function is $y=\frac{1}{2}{x}^2+3$

Calculation:

Function is given as

  $y=\frac{1}{2}{x}^2+3$

Graph of the function is as follows:

  

From the above graph, the minimum value of function is $3$

Conclusion:

Hence, minimum value of function is $3$