Question

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

Answer 1

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

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

Answer 2

the 1st one

Answer 3

@jim_thompson5910

Answer 4

if we replace x with 0, what result do you get

\[\Large y = \sqrt{x-2}\]
\[\Large y = \sqrt{0-2}\]
\[\Large y = ???\]

Answer 5

-2 ?

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

i typed sqrt -2 not 0-2

Answer 11

which calculator are you using?

Answer 12

we wouldnt include any negative numbers in sqrt then

Answer 13

yes you cannot have negative numbers under the square root

eg: \(\Large \sqrt{-1}\) is not allowed

Answer 14

a scientific calculator

Answer 15

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

Answer 16

ok so i wot put any negatives then thx

Answer 17

i get -3

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

yep

Answer 22

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

Answer 23

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

Answer 24

the square root of 0 is 0

Answer 25

your calculator should be able to calculate that

if not, then use this calculator

http://web2.0calc.com/

Answer 26

nevermind i got it

Answer 27

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

Answer 28

thank you for helping me :)

Answer 29

it would be 4

Answer 30

the `x-2` part is 4 when x = 6

but I want the value of y

\[\Large y = \sqrt{x-2}\]
\[\Large y = \sqrt{6-2}\]
\[\Large y = \sqrt{4}\]
\[\Large y = ??\]

Answer 31

oh srry it would be 2

Answer 32

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