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Exploring Parabolas

Erin Mueller

 

 

 

The parabola  will yield the following graph;

 

 

 

But what happens when we alter the variable x? Suppose we replace each x in our original equation with x-4 so that we now have . Look what happens now.

 

When looking at the above graph, one can see that the vertex of the graph has shifted 4 units to the right.

This function can be generalized in the form . By changing our value for b, the vertex moves up and down. The value of b shifts the graph left and right. 

 

Lets suppose we change the equation of our parabola to .

 

 

The parabola above now has vertex (4,4). We can also have the same graph open downward (concave) by changing a single value in our equation.

 

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By placing a (-) in front of the leading coefficient (2), our parabola will now open down.

 

 

 

 

We can now change the equation to produce the two graphs above that share the same vertex.

 

 

 

 

 

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