https://file.aiquickdraw.com/mathbot/file/1726785077867ptz8yb1t.jpg

The equation presented in the image is:

\[
y = x^2 - 10x + 25
\]

This is a quadratic equation. To determine the values of \( y \) for different values of \( x \), we simply substitute the values of \( x \) into the equation and solve for \( y \).

Here’s the table with the provided and missing values:

| \( x \) | \( y \) |
|--------|---------|
|   0    |    ?    |
|   1    |    ?    |
|   2    |    ?    |
|   3    |    6    |
|   4    |    ?    |
|   8    |    ?    |

Let’s calculate the missing values for \( y \).

1. **When \( x = 0 \):**
\[
y = 0^2 - 10(0) + 25 = 25
\]

2. **When \( x = 1 \):**
\[
y = 1^2 - 10(1) + 25 = 1 - 10 + 25 = 16
\]

3. **When \( x = 2 \):**
\[
y = 2^2 - 10(2) + 25 = 4 - 20 + 25 = 9
\]

4. **When \( x = 4 \):**
\[
y = 4^2 - 10(4) + 25 = 16 - 40 + 25 = 1
\]

5. **When \( x = 8 \):**
\[
y = 8^2 - 10(8) + 25 = 64 - 80 + 25 = 9
\]

### Filled table:

| \( x \) | \( y \) |
|--------|---------|
|   0    |    25   |
|   1    |    16   |
|   2    |    9    |
|   3    |    6    |
|   4    |    1    |
|   8    |    9    |

Let me know if you want more detailed steps or explanations!

Here are 5 related questions for you to explore:
1. How do we factor quadratic expressions like \( x^2 - 10x + 25 \)?
2. Can you find the vertex of the parabola represented by \( y = x^2 - 10x + 25 \)?
3. How would you solve \( x^2 - 10x + 25 = 0 \)?
4. What is the axis of symmetry for the quadratic equation \( y = x^2 - 10x + 25 \)?
5. How would you graph the equation \( y = x^2 - 10x + 25 \) using the vertex form?

**Tip**: The equation \( y = x^2 - 10x + 25 \) can be rewritten as \( y = (x - 5)^2 \), which is a perfect square! This makes it easier to analyze graphically.

For the following equation, determine the values of the missing entries. y = x^2 - 10x + 25. Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.

Solve the quadratic equation y = x^2 - 10x + 25 by substituting values for x to find the corresponding y values. Learn step-by-step how to fill in the missing entries for x = 0, 1, 2, 4, and 8 in this algebraic problem, perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation