Chapter 10, Problem 106RE

To determine

To graph: the given solution set and find the coordination of vertices and determine whether the solution is bounded or not.

Answer to Problem 106RE

  

The coordination of vertices is (4,20) and (-4,20)

The solution set is bounded by graph

Explanation of Solution

Given:

  $y-x^2=4$

  $y=20$

Calculation:

We take

  $y-x^2=4\mathrm{.................}\left(1\right)$

  $y=20\mathrm{..................}\left(2\right)$

From equation (1), we have

  $x^2=(y-4)$

  $x^2=y-4$

This is a parabola with vertex (0,4)

From equation (2), we have

  $y=20$

which is a straight line parallel to the $x$ -axis

Substituting $y=20$ into equation $(1),$ we get

  $20-x^2=4$

  $x^2=16$

  $x=\pm 4$

(4,20) and (-4,20) are the points where the parabola and the line intersect

The solution set is bounded by graph

  

Conclusion:

Therefore, the coordination of vertices is (4,20) and (-4,20)

The solution set is bounded by graph