To find: the coordinates of all the vertices and determine whether the solution set bounds or not.
Answer to Problem 29E
The vertices are
The solution set is bounded
Explanation of Solution
Given:
Calculation:
We obtain the equation of the parabola from the given inequality as
Some points on the parabola
X | -4 | -3 | 0 | 3 | 4 |
Y | -7 | 0 | 9 | 0 | -7 |
Using these points we first draw the graph of this parabola.
We graph the parabola given by the equation that corresponds to the inequality. To determine the graph of the inequality, we need to check our test point. Here, we take (0,0) as test point.
Inequality | Test point (0,0) | Conclusion |
Satisfies inequality |
Since (0,0) is below the parabola
Therefore, graph with shaded region is
Vertices: - The origin
Therefore, the vertices are
From the figure it is clear that the shaded region is bounded. Therefore, the solution set is bounded
Conclusion:
Therefore, the vertices are
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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