Understanding Absolute Value Functions

This video tutorial explains how to find the vertex and axis of symmetry for an absolute value function. It begins by setting the inside part of the function equal to zero to find the x-coordinate of the vertex and the axis of symmetry. The y-coordinate is found by substituting the x-value back into the function. The video provides graphical representations and examples, including functions with positive and negative signs, to illustrate how the graph opens upward or downward. It also introduces a general equation for finding the vertex and axis of symmetry. Additional resources for further learning are provided.

What is the first step in finding the vertex of an absolute value function?

• Set the entire function equal to zero

• Graph the function

• Set the inside part of the function equal to zero

• Find the derivative of the function

How do you determine the y-coordinate of the vertex?

• By setting y equal to zero

• By finding the derivative

• By plugging the x-coordinate back into the function

• By graphing the function

What does the graph of an absolute value function look like if the sign in front is positive?

• It opens downward

• It is a vertical line

• It opens upward

• It is a horizontal line

What is the axis of symmetry for the function 4 - |x - 3|?

• x = 3

• x = 0

• x = 4

• x = -3

How does a negative sign in front of an absolute value function affect its graph?

• It becomes a horizontal line

• It opens downward

• It opens upward

• It becomes a vertical line

What is the x-coordinate of the vertex for the function 3x - 7?

• 7

• 3

• 7/3

• 3/7

In the general form a|x - h| + k, what does 'h' represent?

• The slope of the function

• The axis of symmetry

• The x-coordinate of the vertex

• The y-coordinate of the vertex

What is the vertex of the function 2|x - 5| + 3?

• (3, 5)

• (5, 2)

• (5, 3)

• (2, 3)

What is the axis of symmetry for the function 2|x - 5| + 3?

• x = 2

• x = 5

• x = 0

• x = 3

Where can you find more resources related to this topic?

• In the video description

• In the video thumbnail

• In the comments section

• In the video title