Completing the Square

Multiple Choice

What is the significance of converting a quadratic equation to vertex form by completing the square?

• It helps find the vertex easily

• It makes the equation linear

• It eliminates the x-term

• It gives the roots directly

Multiple Choice

How should you move 10 to the other side of the equation?

• Add 10 to both sides

• Subtract to from both sides

• Divide both sides by 10

• Multiply both sides by 10

Multiple Choice

Which term is the "b" value of the equation x² - 12x – 10 = 0?

• 1

• -12

• 12

• -10

Fill in the Blanks

Fill in the blank: To complete the square for x² - 12x + __ = 10, the value added to both sides is ___

Multiple Choice

What is the vertex of (x-6)² − 46 = 0

• (-46, 0)

• (-6, 46)

• (6, -46)

• (6, 46)

Multiple Choice

What is the axis of symmetry of (x-6)² − 46 = 0 ?

• x = 6

• x = -6

• y = 46

• y = -46

Multiple Choice

What is the minimum value of (x-6)² − 46 = 0

• x = 6

• x = -6

• y = 46

• y = -46

Multiple Select

Which key features of quadratic functions are revealed by the vertex form? (select all that apply)

• vertex

• axis of symmetry

• maximum or minimum value

• y-intercept

Multiple Select

Which steps are necessary to convert a quadratic equation to vertex form by completing the square?

• Isolate x² and x terms

• Add the square of half the x coefficient

• Rewrite as a binomial squared

• All of the above

Multiple Choice

Find the missing value "c" to complete the square.

x² + 6x + ____

• 9

• 12

• 36

• - 9

Multiple Choice

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

• (x-18)²

• (x-9)²

• (x+81)²

• (x+9)²

Multiple Choice

Complete the Square
x² + 6x = 5

• (x + 3)² = 5
• (x + 6)² = 9
• (x + 3)² = 14
• (x + 6)² = 14