What is the first step when rewriting y = 3x² + 9x - 18 in the form y = a(x - h)² +k?

Solution:

We will use the method of completing the square to rewrite the equation y = 3x² + 9x - 18 in the vertex form y = a(x - h)² + k.

Given, y = 3x² + 9x - 18

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

Step 1: Take out 3 as common from the first two terms,

y = 3(x² + 3x) - 18 

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

here it is (-3/2)²

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

y = 3(x² + 3x + (-3/2)²) - 18 - 3(-3/2)² [Multiply by 3 taken out common outside the bracket]

y = 3[x + (3/2)]² - 18 - 27/4

y = 3[x + (3/2)]² - 99/ 4

The vertex form of the equation is 3[x + (3/2)]² - 99/ 4.

What is the first step when rewriting y = 3x² + 9x - 18 in the form y = a(x - h)² +k?

Summary:

The first step when rewriting y = 3x² + 9x - 18 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.