# Which quadrants and axes does f(x)=x-sqrt(x+5) pass through?

Nov 15, 2017

$I$, $I I I$ and $I V$ quadrants and it passes through y-axis at $\left(0 , - \sqrt{5}\right)$ and x-axis at $\left(\frac{\sqrt{21}}{2} + \frac{1}{2} , 0\right)$.

#### Explanation:

graph{x-sqrt(x+5) [-6.407, 7.64, -5.67, 1.356]}

As you can see the graph passes through $I$, $I I I$ and $I V$ quadrants.

To know the y-axis point you have to substitute de $x$ by $0$. So:
f(x)=x-sqrt(x+5) ➝ f(0)=0-sqrt(0+5)=-sqrt(5)≈-2.236
And you get the point $\left(0 , - \sqrt{5}\right)$.

To know the x-axis point(s) you have to equal the function to $0$. So:
$f \left(x\right) = x - \sqrt{x + 5} = 0$
you isolate the variable $x$:
x=sqrt(21)/2+1/2≈2.79
So you get the point $\left(\frac{\sqrt{21}}{2} + \frac{1}{2} , 0\right)$.