Chapter 9.8, Problem 28HP

To determine

To calculate: To find the minimum point of the graph of $y=x^2-6$

Answer to Problem 28HP

The minimum point of the graph is $\left(0,-6\right)$

Explanation of Solution

Given information: Function is $y=x^2-6$

Calculation:

Function is given as

  $y=x^2-6$

When $x=0$

  $y={\left(0\right)}^2-6=0-6=-6$

When $x=1$

  $y={\left(1\right)}^2-6=1-6=-5$

When $x=-1$

  $y={\left(-1\right)}^2-6=1-6=-5$

When $x=2$

  $y={\left(2\right)}^2-6=4-6=-2$

When $x=-2$

  $y={\left(-2\right)}^2-6=4-6=-2$

When $x=3$

  $y={\left(3\right)}^2-6=9-6=3$

When $x=-3$

  $y={\left(-3\right)}^2-6=9-6=3$

Function table is

x	y
-3	3
-2	-2
1	-5
0	-6
1	-5
2	-2
3	3

Plotting the points on graph:

  

From the above graph, the minimum point of the graph is $\left(0,-6\right)$

Conclusion:

Hence, the minimum point of the graph is $\left(0,-6\right)$