Math Problem Statement

Graph the equation y = |x| - 2. Find the following y-values. Then choose the correct graph of the equation.

Solution

The problem asks you to graph the equation y=x2y = |x| - 2 and find the corresponding yy-values for the given xx-values: x=3,2,1,0,1,2,3x = -3, -2, -1, 0, 1, 2, 3.

Step-by-Step Solution:

  1. Understand the Equation: The equation y=x2y = |x| - 2 involves the absolute value function x|x|, which always returns a non-negative value. The term 2-2 shifts the graph downward by 2 units.

  2. Calculate yy-values:

    • For x=3x = -3: y=32=32=1y = |-3| - 2 = 3 - 2 = 1
    • For x=2x = -2: y=22=22=0y = |-2| - 2 = 2 - 2 = 0
    • For x=1x = -1: y=12=12=1y = |-1| - 2 = 1 - 2 = -1
    • For x=0x = 0: y=02=02=2y = |0| - 2 = 0 - 2 = -2
    • For x=1x = 1: y=12=12=1y = |1| - 2 = 1 - 2 = -1
    • For x=2x = 2: y=22=22=0y = |2| - 2 = 2 - 2 = 0
    • For x=3x = 3: y=32=32=1y = |3| - 2 = 3 - 2 = 1

Completed Table:

xxyy
-31
-20
-1-1
0-2
1-1
20
31

Now you can plot these points on the graph to represent the function y=x2y = |x| - 2.

Would you like any further details or have any questions?

Here are some related questions to deepen your understanding:

  1. How does the graph of y=x2y = |x| - 2 compare to the graph of y=xy = |x|?
  2. What effect does adding or subtracting a constant from x|x| have on its graph?
  3. How would the graph change if the equation was y=x+12y = |x + 1| - 2?
  4. What are the key features of the graph of an absolute value function?
  5. Can you generalize the shape of y=x+cy = |x| + c for any constant cc?

Tip: Remember that the absolute value function x|x| is V-shaped and symmetrical about the y-axis. Adjusting it vertically shifts the entire graph up or down.

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Math Problem Analysis

Mathematical Concepts

Absolute Value Function
Graphing Linear Equations

Formulas

y = |x| - 2

Theorems

Absolute Value Properties

Suitable Grade Level

Grades 6-8