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We are given the quadratic equation \( y = -2x^2 + 4x + 9 \), and we need to complete the table of values by calculating the values for \( A \) and \( B \).

### Step 1: Calculate \( A \) when \( x = -1 \)
Substitute \( x = -1 \) into the equation \( y = -2x^2 + 4x + 9 \):

\[
y = -2(-1)^2 + 4(-1) + 9 = -2(1) - 4 + 9 = -2 - 4 + 9 = 3
\]

So, \( A = 3 \).

### Step 2: Calculate \( B \) when \( x = 2 \)
Substitute \( x = 2 \) into the equation \( y = -2x^2 + 4x + 9 \):

\[
y = -2(2)^2 + 4(2) + 9 = -2(4) + 8 + 9 = -8 + 8 + 9 = 9
\]

So, \( B = 9 \).

### Final Table:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -2 & -1 & 0 & 1 & 2 \\
\hline
y & -7 & 3 & 9 & 11 & 9 \\
\hline
\end{array}
\]

The numbers that replace \( A \) and \( B \) are \( 3 \) and \( 9 \), respectively.

Would you like more details on how these calculations were made, or do you have any questions?

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Here are some related questions you might find useful:
1. How do you find the vertex of a quadratic function?
2. What does the graph of \( y = -2x^2 + 4x + 9 \) look like?
3. How do you calculate the axis of symmetry for a quadratic function?
4. How can you determine the maximum or minimum value of a quadratic function?
5. What is the significance of the discriminant in a quadratic equation?

**Tip:** In a quadratic equation, the coefficient of \( x^2 \) (in this case, -2) determines whether the parabola opens upwards (positive) or downwards (negative).

Copy and complete the table of values for y = -2x^2 + 4x + 9. What numbers replace A and B?

This problem involves completing a table of values for the quadratic equation y = -2x^2 + 4x + 9. Learn how to find the missing values of A and B using substitution. Suitable for students in Grades 9-10.

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