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Graphing Square Root Functions 573 Views


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Description:

Please be advised that Shmoop does not endorse owning a pet Stegosaurus. The character in this video is a professional—do not attempt at home.

Language:
English Language
Common Core Standards:

Transcript

00:04

Graphing Square Root Functions, a la Shmoop. [Tree roots]

00:07

Teddy has been fascinated by dinosaurs for years…

00:10

…which is why he’s super excited that he just got a pet stegosaurus for his birthday.

00:16

However, the initial excitement is wearing off and reality is setting in… he’s going

00:21

to have to take care of this thing. [Dinosaur scratching at a door]

00:23

Steven… that’s the stegosaurus… is whining at the door, and clearly needs to be walked.

00:29

Teddy’s worried about being able to keep up with his new, large friend. [Teddy being dragged around the park by the dinosaur]

00:34

Is there a way he can find out how fast Steven will walk?

00:38

As it just so happens here at Shmoop, Teddy finds a “dinosaurspeed” equation online. [Teddy using a laptop]

00:44

All he has to do now is graph it.

00:46

y equals the square root of t minus 3, where t is time cleverly.. in seconds, and y is feet. Why not...

00:55

To start, let's first check the domain of the equation, or what t-values are possible

01:02

that allow the function to work.

01:04

Since we know the inside of a square root function can't be negative… [Teddy looking at a blackboard]

01:07

…we can set the inside of the equation t-3 to be greater than or equal to 0.

01:15

By adding 3 to both sides, we see that the possible t's of the function are all greater

01:20

than 3.

01:22

Now we can make a table of values.

01:24

We know the graph doesn't exist at any values of t less than 3… [Dinosaur holding up a sign with t less than 3 on it]

01:29

…so we don't even bother trying points less than 3.

01:32

If we plug in t equals 3 to the y equation, we get the square root of 3 minus 3, which

01:38

equals 0.

01:40

If t equals 4, the square root of 4 minus 3 is the square root of 1, which is just 1.

01:49

If t equals 7, we get the square root of 7 minus 3, or the square root of 4, which is 2. [Table of t values and y values]

01:56

If t equals 12, the square root of 12 minus 3 is root 9, which equals 3.

02:03

Notice that we chose t-values that would give us nice, neat y-values....

02:08

Now let's plot these bad boys.

02:10

(3,0), (4,1), (7,2), and (12,3)… and draw a smooth curve through the points. [The values are plotted on a graph]

02:19

Expect square root functions to be curved lines, and don't try to graph a straight line

02:24

through these points.

02:25

Now that Teddy has found that Steven can walk 3 feet in 12 seconds… [Teddy looking happy whilst his dinosaur is desperate to go for a walk]

02:29

...he can rest assured that he’s not going to be dragged all the way from his home to

02:33

the dinosaur park.

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