Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
7. Graphing Absolute Value Functions
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Exercise 63 Page 162

Graph a few absolute value functions with different values of and to see how the vertex changes.

Practice makes perfect
The best way to understand how different transformations change graphs is by graphing a few examples and comparing the differences. Ultimately, we want to know how affects the vertex of the absolute value function.
When the vertex is First let's test a couple of functions, keeping and We can see how the vertex changes from a function where — where we already know that the vertex is — to functions with and This will give us an idea of how changes the vertex.

As shown above, when the vertex becomes

When the vertex becomes Let's compare these functions and vertices.

Vertex

We can see that we can create the coordinate of the vertex by dividing or by We can graph one more function with different values for and to confirm this. Let's graph the function

The vertex of this function is Since we can conclude that we are dividing by Now we can write a general form for the vertex.