6-5B Graphing Absolute Value Equations Algebra 1 Glencoe McGraw-HillLinda Stamper

Graphs of Absolute Value Equations An absolute Value equation is Every absolute value equation has a V-shaped graph. x y The V-shape opens up if the value of a is positive. x y The V-shape opens down if the value of a is negative.

Determine whether the graph opens up or down. up down What is the value of “a”?

On a graph that opens up, the vertex is the lowest point. On a graph that opens down, the vertex is the highest point. The vertical line passing through the vertex that divides the graph into two symmetric parts is called the line of symmetry. x y x y axis of symmetry line of symmetry

More Absolute Value Graphs The vertex is the lowest or highest point on the graph. x y x y axis of symmetry line of symmetry

Graphing an Absolute Value Equation 1. Find the x-coordinate of the vertex, by finding the value of x for which x + b = 0 2. Make a table of values. Using x-values, calculate at least two values to the left and two values to the right of the vertex. 3. Plot the points given in the table and draw a V- shaped graph (opening up or down) through the points. Note: If all of your values are on one side of the vertex, you will graph a line.

Find the coordinates of the vertex of the graph. The absolute value equations is Set the expression inside the absolute value bars equal to zero and solve for x. The y coordinate of the vertex is the value given for c. Answer is an ordered pair.

Find the coordinates of the vertex of the graph. Example 1 Example 2

Graphing an Absolute Value Equation 1. Find the x-coordinate of the vertex, by finding the value of x for which x + b = 0 2. Make a table of values. Using x-values, calculate at least two values to the left and two values to the right of the vertex. 3. Plot the points given in the table and draw a V- shaped graph (opening up or down) through the points. Note: If all of your values are on one side of the vertex, you will graph a line.

Sketch the graph of Make a table of values. vertex  To avoid graphing fractions, choose values that will create absolute values divisible by two. Find the vertex. (-4,-2)

Sketch the graph of Make a table of values. vertex  Find the vertex. (-4,-2) The “y” values will matchy, matchy!

Sketch the graph of Make a table of values. vertex  If “a” is a whole number, choose values in numerical order! Find the vertex. (-4,-2)

Sketch the graph for each of the following. Example 3 Example 4 Example 5

Will the graph open up or down? Example 3 Sketch the graph of Find the x-coordinate of the vertex. What is the value for “c”? What is the ordered pair for the vertex? Set the expression inside the absolute value bars equal to zero and solve for x.

Reminder: When evaluating the absolute value expression, the amount will always be positive. Why? Example 3 Sketch the graph of Make a table of values. vertex 

Example 3 Sketch the graph of Make a table of values. vertex  matchy, matchy !

Example 3 Sketch the graph of Make a table of values. x y When constructing your ray, it may be helpful to begin at the vertex. vertex 

Sketch the graph for each of the following. Example 3 Example 4 Example 5

Will the graph open up or down? Example 4 Sketch the graph of Find the x-coordinate of the vertex. Set the expression inside the absolute value bars equal to zero and solve for x.

Since the negative sign is outside the absolute value bars, the value of y can be negative. Example 4 Sketch the graph of Make a table of values. vertex 

Example 4 Sketch the graph of Make a table of values. vertex  matchy, matchy !

Example 4 Sketch the graph of Make a table of values. x y How does this graph compare to the first graph? vertex 

Will the graph open up or down? Example 5 Sketch the graph of Find the x-coordinate of the vertex. Set the expression inside the absolute value bars equal to zero and solve for x.

Example 5 Sketch the graph of Make a table of values. x y The vertex shifted 2 spaces to the right (2,0). How does this graph compare to the first graph? vertex  matchy, matchy !

Sketch the graph for each of the following. Example 6 Example 7 Example 8 Example 9 Example 10

Example 6 x y The vertex shifted 4 spaces to the left (–4,0). How does this graph compare to the first graph? vertex

Example 7 x y The vertex shifted 4 spaces upward (0,4). How does this graph compare to the first graph? vertex

3 is a multiplier of the absolute value expression. Example 8 x y The value of “a” made the V narrower. How does this graph compare to the first graph? vertex 

Choose values for x that will result in whole number values for y. Example 9 x y

Example 10 x y

6-A11 Pages # 27-30, and Handout A–11.