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The equation given is \( y = x^3 + 5x - 4 \), and you're asked to complete the table by finding the values of \( y \) corresponding to specific values of \( x \).

The table provides:

\[
\begin{array}{c|cccccc}
x & -2 & -1 & 0 & 1 & 2 \\
\hline
y & -22 & A & B & 2 & C \\
\end{array}
\]

To find the missing values \( A \), \( B \), and \( C \), we need to substitute the corresponding \( x \)-values into the equation \( y = x^3 + 5x - 4 \).

1. **For \( A \), when \( x = -1 \):**
   \[
   y = (-1)^3 + 5(-1) - 4 = -1 - 5 - 4 = -10
   \]
   So, \( A = -10 \).

2. **For \( B \), when \( x = 0 \):**
   \[
   y = (0)^3 + 5(0) - 4 = -4
   \]
   So, \( B = -4 \).

3. **For \( C \), when \( x = 2 \):**
   \[
   y = (2)^3 + 5(2) - 4 = 8 + 10 - 4 = 14
   \]
   So, \( C = 14 \).

The completed table is:

\[
\begin{array}{c|cccccc}
x & -2 & -1 & 0 & 1 & 2 \\
\hline
y & -22 & -10 & -4 & 2 & 14 \\
\end{array}
\]

Would you like further details or have any questions?

Here are 5 related questions to expand this topic:
1. How would the table change if the equation was \( y = x^3 + 2x - 4 \)?
2. What happens to the graph of the function \( y = x^3 + 5x - 4 \) when you shift the constants?
3. How can you determine the behavior of a cubic function based on the sign of its leading coefficient?
4. What is the significance of the cubic term \( x^3 \) in shaping the curve of the function?
5. How would you graph this function manually?

**Tip:** Always double-check your substitution steps to ensure accuracy, especially with signs in cubic and linear terms.

Copy and complete the table of values for y = x^3 + 5x - 4. What numbers replace A, B, and C?

This problem involves solving the cubic function y = x^3 + 5x - 4 by substituting values of x to find corresponding values of y. Complete the table of values for x = -2, -1, 0, 1, 2, filling in A, B, and C. Suitable for Grades 10-12.

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