Evaluate the expression negative 2 left parenthesis x minus 4 right parenthesis squared space plus space 11 when x = 1.

To evaluate the given expression \(-2(x - 4)^2 + 11\) when \(x = 1\), we will substitute \(x = 1\) into the expression and simplify.

Here are the steps:

1. Substitute \(x = 1\) into the expression:

   \[
   -2(1 - 4)^2 + 11
   \]

2. Simplify the expression inside the parentheses:

   \[
   1 - 4 = -3
   \]

   So the expression now is:

   \[
   -2(-3)^2 + 11
   \]

3. Calculate \((-3)^2\):

   \[
   (-3)^2 = 9
   \]

   So the expression now is:

   \[
   -2 \cdot 9 + 11
   \]

4. Multiply \(-2\) by \(9\):

   \[
   -2 \cdot 9 = -18
   \]

   So the expression now is:

   \[
   -18 + 11
   \]

5. Add \(-18\) and \(11\):

   \[
   -18 + 11 = -7
   \]

Thus, the value of the expression \(-2(x - 4)^2 + 11\) when \(x = 1\) is \(-7\).

Would you like more details or have any questions?

Here are five related questions to consider:

1. How would the expression change if \(x\) were a different value?
2. What is the general form of the expression after expanding \(-2(x - 4)^2 + 11\)?
3. How does the graph of \(y = -2(x - 4)^2 + 11\) look, and what are its vertex and axis of symmetry?
4. How would you solve for \(x\) if the expression equals zero?
5. How does changing the coefficient \(-2\) affect the shape of the parabola?

**Tip:** When working with expressions involving squares, always remember to handle negative signs carefully, especially when squaring negative numbers, as \((-a)^2\) is positive.

Learn how to evaluate the expression -2(x - 4)^2 + 11 when x = 1 with a detailed step-by-step solution. This problem involves algebraic manipulation, substitution, and understanding of quadratic expressions. Suitable for Grades 9-12.

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