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

Answer: The first step is to factor out the coefficient of x² (3) from the first two terms, giving y = 3(x² + 3x) – 18.

## Understanding the Vertex Form

Rewriting a quadratic equation in vertex form, y = a(x – h)² + k, involves completing the square. The first step is to factor the leading coefficient (a) from the x² and x terms if a is not 1. This sets the stage for completing the square in the next steps, eventually leading to a form that easily shows the vertex of the parabola represented by the quadratic equation. This technique is crucial in analyzing the properties of quadratic functions and in solving optimization problems.

## FAQ on Understanding the Vertex Form

### How do you find the vertex of a parabola in standard form?

Convert the equation to vertex form and the vertex will be (h, k).

### What is the significance of ‘a’ in the vertex form?

a’ determines the parabola’s opening direction and its width.

### Why is completing the square important in converting to vertex form?

Completing the square reveals the vertex of the parabola, making it easier to analyze and graph.

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