What is the first step when rewriting y = 6x² + 18x + 14 in the form y = a(x - h)² + k?

Solution:

We will use the method of completing the square to rewrite the equation y = 6x² + 18x + 14 in the vertex form y = a(x - h)² + k.

Given, y = 6x² + 18x + 14

Our aim is to make the first two terms a perfect square trinomial.

Step 1: Take out 6 as common factor from the first two terms,

y = 6(x² + 3x) + 14

Step 2: Take the negative half of the coefficient of x, and square it

(-3/2)²

Step 3: Add and subtract the number from the equation.

y = 6(x² + 3x + (-3/2)²) + 14 - 6(-3/2)² [Multiply by 6 taken out a common outside the bracket]

y = 6[x + (3/2)]² + 14 - 27/2

y = 6[x +(3/2)]² + 1/2

The vertex form of the equation is 6[x + (3/2)]² + 1/2.

What is the first step when rewriting y = 6x² + 18x + 14 in the form y = a(x - h)² + k?

Summary:

The first step when rewriting y = 6x² + 18x + 14 in the form y = a(x - h)² + k is to make the first two terms as a perfect square trinomial by completing the square.