https://file.aiquickdraw.com/mathbot/file/17291729287299ktonxbz.jpg

To convert the quadratic equation \( y = x^2 + 8x - 6 \) into vertex form, we need to complete the square.

Here's the step-by-step process:

### 1. Start with the given equation:
\[
y = x^2 + 8x - 6
\]

### 2. Factor out the constant term (which is \(-6\)) for now, and focus on the quadratic and linear terms:
\[
y = (x^2 + 8x) - 6
\]

### 3. Complete the square:
To complete the square, take half of the coefficient of \(x\), which is 8, divide it by 2, and then square it:
\[
\left( \frac{8}{2} \right)^2 = 16
\]

Now, add and subtract 16 inside the parentheses:
\[
y = (x^2 + 8x + 16 - 16) - 6
\]
\[
y = ((x + 4)^2 - 16) - 6
\]

### 4. Simplify the equation:
Now, simplify the constants:
\[
y = (x + 4)^2 - 22
\]

Thus, the equation in vertex form is:
\[
y = (x + 4)^2 - 22
\]

### Answer:
The correct option is the first one:
\[
y = (x + 4)^2 - 22
\]

Would you like further clarification on any part of the solution?

Here are 5 follow-up questions to deepen your understanding:

1. How does completing the square help in converting to vertex form?
2. What is the vertex of the parabola \( y = x^2 + 8x - 6 \)?
3. How do the values of \( h \) and \( k \) in vertex form \( y = (x - h)^2 + k \) affect the graph?
4. Can you use another method to find the vertex without completing the square?
5. How can you verify your solution by expanding the vertex form back into standard form?

**Tip:** Completing the square is an essential algebraic technique that helps in transforming quadratic equations into a more manageable form, revealing key properties like the vertex.

What is the vertex form of the quadratic equation y = x^2 + 8x - 6?

Learn how to convert the quadratic equation y = x^2 + 8x - 6 to its vertex form by completing the square. This process involves algebraic manipulation to reveal the vertex. Suitable 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