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

- lexy148

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

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- jim_thompson5910

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

- lexy148

the 1st one

- lexy148

@jim_thompson5910

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## More answers

- jim_thompson5910

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

- lexy148

-2 ?

- 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

- jim_thompson5910

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

- lexy148

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

- jim_thompson5910

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

- lexy148

i typed sqrt -2 not 0-2

- jim_thompson5910

which calculator are you using?

- lexy148

we wouldnt include any negative numbers in sqrt then

- jim_thompson5910

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

- lexy148

a scientific calculator

- jim_thompson5910

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

- lexy148

ok so i wot put any negatives then thx

- lexy148

i get -3

- 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

- 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

- lexy148

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

- jim_thompson5910

yep

- jim_thompson5910

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

- lexy148

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

- jim_thompson5910

the square root of 0 is 0

- jim_thompson5910

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

- lexy148

nevermind i got it

- jim_thompson5910

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

- lexy148

thank you for helping me :)

- lexy148

it would be 4

- jim_thompson5910

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

- lexy148

oh srry it would be 2

- 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

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