Answer :
Certainly! Let's walk through the steps to evaluate the expression \( -x^2 \) for the given values of \( x \).
### Part (a): When \( x = 4 \)
1. Write down the expression: \( -x^2 \).
2. Substitute \( x = 4 \) into the expression: \( -(4)^2 \).
3. Calculate \( 4^2 \):
[tex]\[ 4^2 = 16 \][/tex]
4. Apply the negative sign:
[tex]\[ -(4^2) = -16 \][/tex]
So, when \( x = 4 \), the value of the expression \( -x^2 \) is \( -16 \).
### Part (b): When \( x = -2 \)
1. Write down the expression: \( -x^2 \).
2. Substitute \( x = -2 \) into the expression: \( -(-2)^2 \).
3. Calculate \( (-2)^2 \):
[tex]\[ (-2)^2 = 4 \][/tex]
4. Apply the negative sign:
[tex]\[ -((-2)^2) = -4 \][/tex]
So, when \( x = -2 \), the value of the expression \( -x^2 \) is \( -4 \).
To summarize:
- For \( x = 4 \), \( -x^2 = -16 \).
- For [tex]\( x = -2 \)[/tex], [tex]\( -x^2 = -4 \)[/tex].
### Part (a): When \( x = 4 \)
1. Write down the expression: \( -x^2 \).
2. Substitute \( x = 4 \) into the expression: \( -(4)^2 \).
3. Calculate \( 4^2 \):
[tex]\[ 4^2 = 16 \][/tex]
4. Apply the negative sign:
[tex]\[ -(4^2) = -16 \][/tex]
So, when \( x = 4 \), the value of the expression \( -x^2 \) is \( -16 \).
### Part (b): When \( x = -2 \)
1. Write down the expression: \( -x^2 \).
2. Substitute \( x = -2 \) into the expression: \( -(-2)^2 \).
3. Calculate \( (-2)^2 \):
[tex]\[ (-2)^2 = 4 \][/tex]
4. Apply the negative sign:
[tex]\[ -((-2)^2) = -4 \][/tex]
So, when \( x = -2 \), the value of the expression \( -x^2 \) is \( -4 \).
To summarize:
- For \( x = 4 \), \( -x^2 = -16 \).
- For [tex]\( x = -2 \)[/tex], [tex]\( -x^2 = -4 \)[/tex].
