Chapter 1, Problem 7RE

To determine

To graph: the given equation

Answer to Problem 7RE

  

Explanation of Solution

Given:

  $y=x^2+4$

Calculation:

In order to find the $x$ -intercept, let $y=0$ and solve for $x$

  $\begin{array}{l}y=x^2+4\\ 0=x^2+4\end{array}$

Subtract 4 from both the sides.

  $\begin{array}{l}{x}^2+4-4=0-4\\ x^2=-4\end{array}$

Since the square of a number cannot be negative, there is no real solution for $x$ .

Therefore, there is no $x$ -intercept.

For finding the $y$ -intercept, let $x=0$ and solve for $y$ .

  $y=0^2+4$

  $y=4$

The $y$ -intercept is 4

For plotting the graph, substitute various values of $x$ in the equation to obtain some points onthe graph.

x	$y=x^2+4$	$(x,y)$
-1	5	$(-1,5)$
-2	8	$(-2,8)$
1	5	$(1,5)$
2	8	$(2,8)$

Since $x^2\ge 0$ for all x, the y will be $y\ge -1$ from the equation $y=x^2+4$

Use this information, the intercepts, and the points from the table to obtain the graph of

  $y=x^2+4$ .

  

Conclusion:

Thus, the graph is drawn.