Question

y = x² + 5
column by column
x | x² | y = x² + 5
-3 | |
-2 | |
-1 | |
0 | |
1 | |
2 | |
3 | |

Explanation:

Step1: Calculate \( x^2 \) for \( x = -3 \)

We know that for any real number \( a \), \( (-a)^2=a^2 \). So when \( x = - 3 \), we calculate \( x^{2}=(-3)^{2}\). By the definition of squaring a negative number, \( (-3)\times(-3) = 9 \). So \( x^{2}=9 \) when \( x=-3 \).

Step2: Calculate \( y=x^{2}+5 \) for \( x = - 3 \)

We already found that \( x^{2}=9 \) when \( x = - 3 \). Now substitute \( x^{2}=9 \) into the equation \( y=x^{2}+5 \). Then \( y=9 + 5\). Adding 9 and 5, we get \( y = 14 \).

Answer:

For the \( x^{2} \) column (when \( x=-3 \)): \( 9 \); For the \( y=x^{2}+5 \) column (when \( x = - 3 \)): \( 14 \)