## lexy148 one year ago How do you graph and solve for y= square root x-2 if the x points are 0,-1,-2,1,2

1. jim_thompson5910

is the equation this? $\Large y = \sqrt{x-2}$ or this?$\Large y = \sqrt{x}-2$

2. lexy148

the 1st one

3. lexy148

@jim_thompson5910

4. jim_thompson5910

if we replace x with 0, what result do you get $\Large y = \sqrt{x-2}$ $\Large y = \sqrt{0-2}$ $\Large y = ???$

5. lexy148

-2 ?

6. jim_thompson5910

you'll have $\Large \sqrt{-2}$ BUT you cannot take the square root of a negative number. The result isn't a real number. So the calculator should say NAN or undefined or something

7. jim_thompson5910

did you type in sqrt(0-2) or sqrt(-2) into your calculator?

8. lexy148

yeah thats what it said when i did it in the calculator

9. jim_thompson5910

so because of this error, we don't include x = 0 in the domain

10. lexy148

i typed sqrt -2 not 0-2

11. jim_thompson5910

which calculator are you using?

12. lexy148

we wouldnt include any negative numbers in sqrt then

13. jim_thompson5910

yes you cannot have negative numbers under the square root eg: $$\Large \sqrt{-1}$$ is not allowed

14. lexy148

a scientific calculator

15. jim_thompson5910

ok, what happens when you replace x with -1 instead of 0? what result do you get?

16. lexy148

ok so i wot put any negatives then thx

17. lexy148

i get -3

18. jim_thompson5910

the goal is to have x-2 never be negative so we can force it to be 0 or positive, ie force it to be greater than or equal to 0 $\Large x-2\ge 0$ solve for x to get $\Large x\ge 2$ so you are allowed to input values of x that are either 2 or larger than 2

19. jim_thompson5910

you'll find that $\Large \sqrt{-3}$ isn't a real number. So x = -1 isn't allowed to be an input either

20. lexy148

ok i see so only numbers 2 or more, no negatives

21. jim_thompson5910

yep

22. jim_thompson5910

if x = 2, then what is the value of y?

23. lexy148

ok thank you and how would you sqrt 0 since 2-2 is 0

24. jim_thompson5910

the square root of 0 is 0

25. jim_thompson5910

your calculator should be able to calculate that if not, then use this calculator http://web2.0calc.com/

26. lexy148

nevermind i got it

27. jim_thompson5910

ok one more: if x = 6, then what is the value of y?

28. lexy148

thank you for helping me :)

29. lexy148

it would be 4

30. jim_thompson5910

the x-2 part is 4 when x = 6 but I want the value of y $\Large y = \sqrt{x-2}$ $\Large y = \sqrt{6-2}$ $\Large y = \sqrt{4}$ $\Large y = ??$

31. lexy148

oh srry it would be 2

32. jim_thompson5910

correct, so when x = 6, the value of y is y = 2 that means we have the point (6,2) earlier you found that when x = 2, the value of y was y = 0 so the point (2,0) You make a table of x,y values and plot each ordered pair as a point on the xy grid. Once you have enough points, you can draw a curve through them all to complete the graph