Chapter 9.8, Problem 27HP

To determine

To calculate: To find the maximum point of the graph of $y=-x^2+7$

Answer to Problem 27HP

The maximum point of the graph is $\left(0,7\right)$

Explanation of Solution

Given information: Function is $y=-x^2+7$

Calculation:

Function is given as

  $y=-x^2+7$

When $x=0$

  $y=-{\left(0\right)}^2+7=0+7=7$

When $x=1$

  $y=-{\left(1\right)}^2+7=-1+7=6$

When $x=-1$

  $y=-{\left(-1\right)}^2+7=-1+7=6$

When $x=2$

  $y=-{\left(2\right)}^2+7=-4+7=3$

When $x=-2$

  $y=-{\left(-2\right)}^2+7=-4+7=3$

When $x=3$

  $y=-{\left(3\right)}^2+7=-9+7=-2$

When $x=-3$

  $y=-{\left(-3\right)}^2+7=-9+7=-2$

Function table is

x	y
-3	-2
-2	3
1	6
0	7
1	6
2	3
3	-2

Plotting the points on graph:

  

From the above graph, the maximum point of the graph is $\left(0,7\right)$

Conclusion:

Hence, the maximum point of the graph is $\left(0,7\right)$