Completing the Square for Parabolas in Vertex Form

The video tutorial explains how to use the method of completing the square to convert a quadratic equation into vertex form. It begins with an introduction to vertex form and its differences from standard form. The instructor then details the process of completing the square, emphasizing the importance of having a coefficient of one for x squared. Two examples are provided to illustrate the conversion process and the identification of transformations from the parent function. The video concludes with a prompt for students to practice the method and prepare questions for class discussion.

What is the main difference between standard form and vertex form of a quadratic equation?

• Standard form is used for linear equations.

• Vertex form shows the vertex of the parabola.

• Standard form shows the vertex of the parabola.

• Vertex form is used for linear equations.

In vertex form, what does the 'h' value represent?

• Vertical shift

• Reflection

• Stretch or compression

• Horizontal shift

What is the first step in completing the square for a quadratic equation?

• Factor the trinomial

• Add b/2 squared to both sides

• Move the constant term to the other side

• Divide by the coefficient of x^2 if it is not 1

When completing the square, what do you add to both sides of the equation?

• b squared

• b/2

• b/2 squared

• b/4

In Example A, what is the vertex of the equation y = x^2 + 6x - 1 after converting to vertex form?

• (3, 8)

• (-3, -8)

• (-3, 8)

• (3, -8)

What horizontal shift occurs in Example A?

• 3 units right

• 8 units down

• 3 units left

• 8 units up

In Example B, what is the first step to handle the non-unitary leading coefficient?

• Move the constant term to the other side

• Divide everything by the leading coefficient

• Add b/2 squared to both sides

• Factor the trinomial

What is the vertex of the equation y = -2x^2 - 16x + 2 after converting to vertex form?

• (4, 30)

• (-4, -30)

• (4, -30)

• (-4, 30)

What transformation does the negative sign in front of the leading coefficient indicate?

• Horizontal shift

• Reflection in the x-axis

• Stretch by a factor of 2

• Vertical shift

What should students do if they have questions about the material covered?

• Ignore them

• Ask a friend

• Jot them down and bring them to class

• Search online