Evaluate the algebraic expression for the given value of the variable.
negative x squared minus 2−x2−2​; x equals negative 4x=−4

Let's evaluate the given algebraic expression for \( x = -4 \). 

The expression is: 

\[
-x^2 - 2
\]

Substitute \( x = -4 \) into the expression:

\[
-(-4)^2 - 2
\]

First, calculate \( (-4)^2 \):

\[
(-4)^2 = 16
\]

Now substitute \( 16 \) back into the expression:

\[
-16 - 2
\]

Finally, simplify:

\[
-16 - 2 = -18
\]

So, the value of the expression when \( x = -4 \) is:

\[
\boxed{-18}
\]

Would you like any more details on this? Here are some follow-up questions you might find interesting:

1. What is the difference between evaluating \( -x^2 \) and \( (-x)^2 \)?
2. How does the order of operations affect evaluating this expression?
3. What happens when you substitute a positive value for \( x \) in this expression?
4. How would this expression change if you added another term, say \( + 3x \)?
5. Can you graph the expression \( -x^2 - 2 \) and analyze its shape?

**Tip**: Always pay attention to whether the negative sign is inside or outside the parentheses when dealing with exponents. It makes a big difference!

Evaluate the algebraic expression for the given value of the variable. -x^2 - 2 when x = -4

Learn how to evaluate the algebraic expression -x^2 - 2 when x = -4 with a step-by-step breakdown. This problem involves key concepts such as algebra, exponents, and order of operations. Suitable for students in Grades 7-9.

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