Completing the Square: A Comprehensive Guide

What is the first step in completing the square?

• Factor out the coefficient of x^2

• Group the x^2 and x terms together

• Simplify the equation

• Add and subtract the same value

When completing the square, what do you do after grouping the x^2 and x terms?

• Add a constant to both sides

• Factor out the coefficient of x^2

• Combine like terms

• Take half of the coefficient of x and square it

In the example x^2 - 8x + 16, what is the value added to complete the square?

• 8

• 16

• 4

• 64

What is the vertex form of the equation x^2 - 8x + 18?

• (x + 4)^2 + 2

• (x - 4)^2 - 2

• (x - 4)^2 + 2

• (x + 4)^2 - 2

How do you handle a negative sign when completing the square?

• Ignore it

• Factor it out

• Multiply it by the coefficient of x

• Add it to the constant term

What is the magic number added when completing the square for x^2 - 3x?

• 9

• 9/4

• 3/2

• 25/4

What is the vertex form of the equation x^2 - 3x - 2?

• (x - 3/2)^2 - 13/2

• (x + 3/2)^2 - 13/2

• (x - 3/2)^2 + 13/2

• (x + 3/2)^2 + 13/2

What is the vertex of the equation x^2 - 12x + 39 in vertex form?

• (6, 3)

• (-6, 3)

• (-6, -3)

• (6, -3)

What additional information does the vertex form of a quadratic equation provide?

• The vertex and direction of the parabola

• The y-intercept

• The x-intercept

• The axis of symmetry

What is the purpose of converting a quadratic equation to vertex form?

• To find the roots

• To simplify the equation

• To easily identify the vertex and graph the equation

• To eliminate fractions