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When \( y = 0 \), the solution for \( x \) in the equation \( y = x^2 - 14x + 49 \) is \( x = 7 \).

Now, I'll find the missing \( y \)-values by substituting the given \( x \)-values (6, 10, and 5) into the equation. Let's proceed with that.The missing values in the table are as follows:

1. For \( x = 6 \), \( y = 1 \).
2. For \( x = 10 \), \( y = 9 \).
3. For \( x = 5 \), \( y = 4 \).

To summarize:
- The missing \( x \)-value when \( y = 0 \) is \( x = 7 \).
- The missing \( y \)-values are 1, 9, and 4 for \( x = 6 \), \( x = 10 \), and \( x = 5 \), respectively.

Would you like more details on the calculations or clarification on any steps?

Here are some related questions you might find interesting:
1. What is the general method for solving quadratic equations?
2. How does completing the square help in solving quadratics?
3. What are the different forms of a quadratic equation?
4. How can we use the quadratic formula for non-integer solutions?
5. What is the significance of the vertex of a parabola in quadratic functions?

**Tip:** Always check whether the discriminant \( b^2 - 4ac \) is non-negative before trying to solve a quadratic equation for real solutions.

For the following equation, determine the values of the missing entries. y = x^2 - 14x + 49. The table represents ordered pairs.

Learn how to solve the quadratic equation y = x^2 - 14x + 49 and find the missing values in the table. Key algebraic concepts include solving for x and determining y-values based on given x-values. Suitable for students in Grades 7-9.

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