Completing the square to convert between quadratic and vertex form

The video tutorial explains how to convert a quadratic equation into vertex form by completing the square. It begins with an introduction to the vertex form and the necessity of completing the square. The instructor then demonstrates factoring out a coefficient and adjusting terms to create a perfect square trinomial. The process involves adding and subtracting terms while considering the impact of multiplication on the equation. Finally, the tutorial concludes with the equation in vertex form, highlighting the vertex and transformations of the graph.

What is the first step in converting a quadratic equation to vertex form?

• Set the equation equal to zero

• Complete the square

• Factor out the constant term

• Multiply by the leading coefficient

When completing the square, what is the result of b divided by 2 squared if b is -6?

• -9

• -3

• 3

• 9

Why is it necessary to multiply the added and subtracted term by the factor outside the parentheses?

• To simplify the equation

• To maintain the equation's balance

• To eliminate the constant term

• To change the equation's form

What is the vertex of the parabola after converting the equation to vertex form?

• (-3, 6)

• (-6, 3)

• (6, 3)

• (3, 6)

How does the graph of the equation transform after converting to vertex form?

• It shifts vertically

• It stretches vertically

• It reflects over the x-axis and is horizontally compressed

• It reflects over the y-axis