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].
