Complete the table by squaring each negative [tex]$x$[/tex]-value listed:
[tex]
\begin{array}{cc}
x & x^2 \\
-2 & \\
-3 & \\
-4 & \\
-5 & \\
-6 & \\
-7 & \\
-8 & \\
-9 & \\
-10 & \\
-11 & \\
\end{array}
[/tex]
Answer (2)
Calculate the square of -2: ( − 2 ) 2 = 4 .
Calculate the square of -3: ( − 3 ) 2 = 9 .
Calculate the square of -4: ( − 4 ) 2 = 16 .
Continue this process for all given x-values to complete the table: The squares are 4, 9, 16, 25, 36, 49, 64, 81, 100, 121. 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121
Explanation
Understanding the Problem We are asked to complete a table by squaring each negative x -value listed. This means we need to calculate x 2 for each given x .
Calculating the Squares Let's calculate the square of each x -value:
( − 2 ) 2 = ( − 2 ) × ( − 2 ) = 4
( − 3 ) 2 = ( − 3 ) × ( − 3 ) = 9
( − 4 ) 2 = ( − 4 ) × ( − 4 ) = 16
( − 5 ) 2 = ( − 5 ) × ( − 5 ) = 25
( − 6 ) 2 = ( − 6 ) × ( − 6 ) = 36
( − 7 ) 2 = ( − 7 ) × ( − 7 ) = 49
( − 8 ) 2 = ( − 8 ) × ( − 8 ) = 64
( − 9 ) 2 = ( − 9 ) × ( − 9 ) = 81
( − 10 ) 2 = ( − 10 ) × ( − 10 ) = 100
( − 11 ) 2 = ( − 11 ) × ( − 11 ) = 121
Completing the Table Now we can complete the table with the calculated x 2 values.
The completed table is:
x \t x 2
-2 4
-3 9
-4 16
-5 25
-6 36
-7 49
-8 64
-9 81
-10 100
-11 121
Final Answer The squares of the given negative x -values are 4, 9, 16, 25, 36, 49, 64, 81, 100, and 121.
Examples
Understanding squares is fundamental in many areas, such as calculating the area of a square or understanding quadratic relationships in physics. For example, if you're designing a square garden that is 5 meters on each side, you need to know that the area is 5 2 = 25 square meters. This concept extends to more complex scenarios, like calculating the kinetic energy of an object, which depends on the square of its velocity.
To complete the table by squaring negative x-values, we calculated the squares of each value from -2 to -11. The squared results are 4, 9, 16, 25, 36, 49, 64, 81, 100, and 121. These calculations illustrate the concept that squaring a negative number results in a positive number.
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