# Homework Help: Explain graph of y=√x

1. Jan 16, 2012

### sharks

The problem statement, all variables and given/known data
Explain graph of y=√x

The attempt at a solution
I've done the graph on an online graphing calculator:

But i don't understand why there is no equivalent reflection below the x-axis, in the 4th quadrant.

From y=√x,
if x=4, then y is either 2 or -2. Correct? Then, why is the value -2 discarded?
Furthermore, if i rewrite the equation y=√x as x=y^2, then the graph does indeed become like this:

2. Jan 16, 2012

### LearninDaMath

I think it has something to do with the fact that including both answers would disqualify its graph from being a function, so by convention, you only use the graph of one of the answers, the positive ones. That is my guess, I could be wrong.

3. Jan 16, 2012

### sharks

4. Jan 16, 2012

### Staff: Mentor

The graph of $y = \sqrt{x}$ is exactly as you show in post 1. Looking at the domain, x must be >= 0. For the range, the square root returns a value >= 0. In your example, if x = 4, y = 2, not -2, because the square root of 4 is 2, not -2.

It is true that 4 has two square roots, but the principal square root, which is indicated by the square root symbol, is nonnegative. For these reasons, the graph of this function appears only in the first quadrant.

5. Jan 16, 2012

### LearninDaMath

Sorry about that. It's still a correct answer, in my opinion. Why else would the graph appear as you present it other than convention, as Mark much, much more precisely explained it. Hopefully I can get an equally precise answer to my most recent thread...I'm just trying to contribute what little I can to others' questions in the meantime :).

6. Jan 16, 2012

### Jorriss

Just try out a few points.

y = sqrt(x). If you plug in x, you get y=1. Not y= +/- 1

7. Jan 16, 2012

### Redbelly98

Staff Emeritus
When you use a calculator to figure out a number's square root, are you bothered that it only gives you a single positive number for the result?

8. Jan 17, 2012

### sharks

I'll use these explanations as they both justify the graph by the conventional value of a square root.

9. Jan 17, 2012

### Mentallic

I think you did well

sharks, do you know the quadratic formula?

10. Jan 20, 2012

### sharks

Hi Mentallic

$$-b \pm \sqrt{b^2 - 4ac} \over 2a$$
Yes, i'm familiar with solving unknowns using that formula. What point are you trying to make?

Last edited: Jan 20, 2012
11. Jan 20, 2012

### Mentallic

Why does it have a $\pm$ symbol if the square root of 4 for example is both 2 and -2? We wouldn't need that symbol there if the square root already produced both values.

12. Jan 20, 2012

### sharks

Good point! I'll add it to the whoever-need-convincing list.

13. Jan 20, 2012