You can combine the equations for stretches and compressions with the equations for translations to write a general form for absolute value functions.
The stretch or compression factor is |a|, the vertex is located at (h, k), and the axis of symmetry is the line
Without graphing, what are the vertex and axis of symmetry of the graph of
Compare
To what should you compare
Compare it to the general form,
The vertex is (2, 4) and the axis of symmetry is
The parent function
Check Check by graphing the equation on a graphing calculator.
What is the equation of the absolute value function?
Step 1 Identify the vertex.
The vertex is at (
Step 2 Identify a.
The slope of the branch to the right of the vertex is
What does the graph tell you about a?
The upside-down V suggests that
Step 3 Write the equation.
Substitute the values of a, h, and k into the general form
What is the equation of the absolute value function?