Chapter 1.2, Problem 25E

To determine

The $x-\text{intercept}$ and $y-\text{intercept}$ of the graph of the equation $y=\sqrt{x+4}$ .

Answer to Problem 25E

The $x-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(-4,0\right)$

The $y-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(0,2\right)$

Explanation of Solution

Given:

The equation $y=\sqrt{x+4}$

Concept Used:

The $x-\text{intercept}$ is a point on the graph where the graph intersects $x-\text{axis}$ i.e., where the $y$ coordinate is zero.

The $y-\text{intercept}$ is a point on the graph where the graph intersects $y-\text{axis}$ i.e., where the $x$ coordinate is zero.

Calculation:

Given the equation $y=\sqrt{x+4}$

For $x-\text{intercept}$ , substituting $y=0$

i.e., $y=\sqrt{x+4}$

i.e., $\begin{array}{c}0=\sqrt{x+4}\\ 0^2={\left(\sqrt{x+4}\right)}^2\text{ Squaring both sides}\\ 0=x+4\\ x=-4\end{array}$

Therefore, $x-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(-4,0\right)$

For $y-\text{intercept}$ , substituting $x=0$

i.e., $y=\sqrt{x+4}$

i.e., $\begin{array}{l}y=\sqrt{x+4}\\ y=\sqrt{0+4}\\ y=\sqrt{4}\\ y=2\end{array}$

Therefore, $y-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(0,2\right)$