ShmoopTube

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

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Teddy has been fascinated by dinosaurs for years…

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

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

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

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

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

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

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

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All he has to do now is graph it.

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

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

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that allow the function to work.

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

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

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

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than 3.

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Now we can make a table of values.

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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]

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

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

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equals 0.

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

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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]

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

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

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Now let's plot these bad boys.

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

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

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through these points.

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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]

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

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the dinosaur park.

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