Find the solutions for each absolute value equation

Find the solutions for each absolute value equation:

Math 8 H Graphing Absolute Value Equations Algebra 1 Glencoe Mc. Graw-Hill Jo. Ann Evans

The ABSOLUTE VALUE of a real number is the distance between the origin and the point representing the real number. The number 5 is five spaces from 0, the origin. |x| = x when x > 0 0 is zero spaces from itself. |0| = 0 The number -3 is three spaces from 0, |x| = -x when x < 0 the origin. Distance is not negative; the absolute value of a number will never be negative.

Graph the equation: x y = |x| y Every absolute value equation will graph into a v-shape. The VERTEX is the point of the v-shaped graph. Some will open up, others will open down.

Graph y = -|x| Graph y = |x - 2| How does this graph differ from y = |x|? vertex x -2 -1 0 1 2 y -2 -1 0 -1 -2 vertex x -2 0 2 4 6 y 4 2 0 2 4

Graph y = |x| + 1 How does this graph differ from y = |x|? vertex x -2 -1 0 1 2 Graph y = |x| - 3 How does this graph differ from y = |x|? y 3 2 1 2 3 vertex x -2 -1 0 1 2 y -1 -2 -3 -2 -1

Graph y = |x + 2| How does this graph differ from y = |x|? vertex x -4 -3 -2 -1 0 Graph y = |x - 1| How does this graph differ from y = |x|? y 2 1 0 1 2 vertex x -1 0 1 2 3 y 2 1 0 1 2

It’s possible to tell what the x value of the vertex will be just by looking at the absolute value equation. The value of x that will make the expression INSIDE the absolute value symbol equal to ZERO will be the x-value of the vertex of the graph. Why is this useful information Knowing the x-value of the vertex will help you to efficiently select x-values for the table of values. You need several values on either side of the vertex in order to see the v-shape appear.

To Sketch the Graph of an Absolute Value Equation: 1. Find the value of x that will make the expression inside the absolute value symbol equal to zero. Place this value of x in the middle of your table of values. 2. Choose two values of x less than this number and two values of x greater than this number. 3. Calculate the corresponding y values and sketch the resulting v-shaped graph. If the x values are evenly spaced on either side of the x value of the vertex, the y values should show a pattern.

Sketch the graph of y = |x + 2| - 3 What value of x will make the expression inside the absolute value sign equal to 0? x -4 y -1 -3 -2 -2 -3 -1 -2 0 -1 -2 -2 is the x value of the vertex. Place it in the middle of the table. Choose 2 values less and 2 values more, evenly spacing them.

Sketch the graph of y = -2|x - 1| + 2 x -1 y -2 0 0 1 2 2 0 3 -2 What value of x will make the expression inside the absolute value sign equal to 0? 1 Place 1 in the middle of the table. Choose 2 values less and 2 values more, evenly spaced. When there’s a negative coefficient before the absolute value symbol, the graph will open down.

What value of x will make the expression inside the absolute value sign equal to 0? Sketch the graph of x -4 y -2 -3 -2. 5 -2 -3 -1 -2. 5 0 -2 -2 Place -2 in the middle of the table. Choose 2 values less and 2 values more, evenly spaced. When there’s a positive coefficient before the absolute value symbol, the graph will open up.

Is there a way to easily tell what the y value of the vertex will be? y = |x| + 1 What will the x value of the vertex be? If x is 0, what is y? 1 0 y = |x - 2| - 5 What will the x value of the vertex be? 2 If x is 2, what is y? -5 What will the x value of the vertex be? If x is -3, what is y? -4 -3 y = 2|x - 1| + 7 What will the x value of the vertex be? If x is 1, what is y? 7 1 y = |x + 3| - 4

What will be the coordinates of the vertex? y = |x| + 3 (0, 3) y = |x + 8| (-8, 0) y = |x| - 5 (0, -5) y = |x + 9| - 14 y = -5|x + 2| y = 2|2 x – 4| + 6 y = -|x – 1| + 5 (-9, -14) (-2, 0) (2, 6) (1, 5)