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Graphing a Horizontal Parabola - Problem 2

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Graphing a sideways parabola on your calculator. So if you look at your calculator and you go to the graph option, you realize that everything is y equals, so when we're dealing with a sideways parabola which is x equals, we're not able to put that directly into our calculator, so in order to put it in what we have to do is solve for y.

So solving it for y is just like solving any other equation, we want to get it up by itself, so subtract 3 over and then we need to take the square root of both sides. Now remember whenever we take the square root and use it as a 2, and we put it in there, we have to include plus or minus. And then to finish this up what we really want to do is add the one around, so we end up with y is equal to plus or minus the square root of x minus 3 plus 1.

And what this plus or minus does is actually one portion is the top part of the graph and one portion is the bottom of the graph. So looking at this, this is just a transformation of a square root graph. The x minus 3 is going to move it forward 3 and the up one is going to move it up 1 and we have one, two, three over and one. The positive branch is going to give us the top part and the negative branch is going to give us the bottom square root function.

Now in order to graph these on your calculator, you really have to put it in as two different functions, the positive square root and the negative square root. The reason being is our calculator can only graph functions and together these don't pass the vertical line test, this is in a function. Individually you split it up to the top half and the bottom half they both are.

So whenever you are trying to graph a sideways parabola on your calculator, solve x for y, make sure you remember your plus and minus when you take the square root and then enter it as two different equations.

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