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We are given the quadratic equation \( y = x^2 + 4x - 1 \) and are asked to complete the table for values of \( y \) when \( x = -3 \), \( -2 \), \( -1 \), \( 0 \), and \( 1 \). Specifically, we need to find the values of \( A \), \( B \), and \( C \).

### Step-by-Step Calculations:

1. **For \( x = -3 \):**
   \[
   y = (-3)^2 + 4(-3) - 1 = 9 - 12 - 1 = -4
   \]
   So, \( A = -4 \).

2. **For \( x = -2 \):**
   \[
   y = (-2)^2 + 4(-2) - 1 = 4 - 8 - 1 = -5
   \]
   This value is already provided in the table as \( y = -5 \).

3. **For \( x = -1 \):**
   \[
   y = (-1)^2 + 4(-1) - 1 = 1 - 4 - 1 = -4
   \]
   So, \( B = -4 \).

4. **For \( x = 0 \):**
   \[
   y = (0)^2 + 4(0) - 1 = -1
   \]
   This value is also provided in the table as \( y = -1 \).

5. **For \( x = 1 \):**
   \[
   y = (1)^2 + 4(1) - 1 = 1 + 4 - 1 = 4
   \]
   So, \( C = 4 \).

### Final Values:
- \( A = -4 \)
- \( B = -4 \)
- \( C = 4 \)

Would you like more details on any part of this solution? 

Here are some related questions to explore:
1. How do we derive the general formula for a quadratic equation?
2. What are the properties of the graph of a quadratic equation like \( y = x^2 + 4x - 1 \)?
3. How can you find the vertex of a quadratic equation?
4. What is the axis of symmetry for this quadratic equation?
5. How do different values of \( x \) affect the behavior of quadratic functions?

**Tip:** Always double-check your work by substituting values back into the original equation!

Copy and complete the table of values for y = x^2 + 4x - 1. What numbers replace A, B, and C?

Learn how to complete the table of values for the quadratic equation y = x^2 + 4x - 1. Find the values of A, B, and C by substituting different x-values into the equation, covering key algebraic concepts. Suitable for students in Grades 8-10.

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