https://file.aiquickdraw.com/mathbot/file/1726092399901rrbiyvfe.jpg

The expression given is:

\[
-2(x - 4)^2 + 11 \quad \text{when} \quad x = 1
\]

Let's break this down step by step to evaluate it for \(x = 1\):

1. Substitute \(x = 1\) into the expression:
   \[
   -2(1 - 4)^2 + 11
   \]

2. Simplify inside the parentheses:
   \[
   1 - 4 = -3
   \]
   So the expression becomes:
   \[
   -2(-3)^2 + 11
   \]

3. Square \(-3\):
   \[
   (-3)^2 = 9
   \]
   Now, the expression is:
   \[
   -2 \times 9 + 11
   \]

4. Multiply \(-2\) by \(9\):
   \[
   -18 + 11
   \]

5. Finally, add \(11\) to \(-18\):
   \[
   -18 + 11 = -7
   \]

Thus, the value of the expression when \(x = 1\) is \(-7\).

The correct answer is **b) -7**.

Would you like further details or have any questions?

Here are some related questions to think about:
1. How does squaring a negative number affect the result?
2. What role does the coefficient \(-2\) play in the final result?
3. What happens if the value of \(x\) was greater than 4?
4. How would the result change if the expression was \(+2(x - 4)^2 + 11\)?
5. How do absolute values relate to operations like squaring and multiplying?

**Tip:** Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) when solving mathematical expressions.

Evaluate the expression -2(x - 4)^2 + 11 when x = 1.

Learn how to evaluate the expression -2(x - 4)^2 + 11 when x = 1. This problem covers essential algebraic concepts like quadratic expressions and following the order of operations (PEMDAS). Suitable for students in Grades 8-10.

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