Let's evaluate the expression $-2(x - 4)^2 + 11$ when $x = 1$.

Step-by-Step Solution:

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 the result: $(-3)^2 = 9$ Now, the expression is: $-2(9) + 11$
4. Multiply: $-2 \times 9 = -18$ So the expression becomes: $-18 + 11$
5. Add the numbers: $-18 + 11 = -7$

Thus, the value of the expression when $x = 1$ is $\boxed{-7}$.

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Would you like a more detailed explanation of any step, or do you have further questions on this topic?

Follow-up Questions:

1. How would the value of the expression change if $x = 2$?
2. Can you explain how squaring a negative number affects the outcome?
3. What is the effect of multiplying the squared term by a negative number?
4. How do parentheses influence the order of operations in expressions like this?
5. What would happen if the expression was written as $-2x^2 + 11$?

Tip: Always remember to follow the correct order of operations (PEMDAS/BODMAS) when simplifying mathematical expressions!