What is the first step when rewriting y = 6x2 + 18x + 14 in the form y = a(x – h)2 + k?
16 must be factored from 18x + 14
x must be factored from 6x2 + 18x
6 must be factored from 6x2 + 14
6 must be factored from 6x2 + 18x

The correct first step in rewriting the equation \( y = 6x^2 + 18x + 14 \) in the form \( y = a(x - h)^2 + k \) is:

**6 must be factored from \( 6x^2 + 18x \).**

Here's why:
- The goal is to complete the square. 
- First, factor out the 6 from the terms involving \(x^2\) and \(x\) (i.e., \(6x^2 + 18x\)) to make the coefficient of \(x^2\) equal to 1, which simplifies the process of completing the square.

So the first step looks like this:
\[
y = 6(x^2 + 3x) + 14
\]

Do you want more details or have any other questions?

Here are 5 related questions:
1. How do you complete the square after factoring out 6?
2. How do you find the vertex \(h\) and \(k\) in the form \(a(x - h)^2 + k\)?
3. Why is completing the square useful for rewriting quadratic equations?
4. What is the next step after factoring the \(6x^2 + 18x\) terms?
5. How can you graph a quadratic equation in vertex form?

**Tip**: Always check that the coefficient of \(x^2\) is 1 before completing the square.

What is the first step when rewriting y = 6x^2 + 18x + 14 in the form y = a(x – h)^2 + k?

Understand the first step in rewriting the quadratic equation y = 6x^2 + 18x + 14 in the form y = a(x – h)^2 + k by factoring 6 from the quadratic and linear terms. This guide covers completing the square, key algebraic concepts, and suitable for students in Grades 9-11.

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