Copy of ML Amp 5.1 Completing the Square (Part One)

Multiple Choice

Which of the following is a perfect-square quadratic expression?

• x^2 + 6x + 9

• x^2 + 5x + 4

• x^2 - 4x + 7

• x^2 + 2x + 8

Multiple Choice

Which of the following expressions is equivalent to (x+5)(x+5) when expanded using the distributive property?

• x^2 + 10x + 25

• x^2 + 25

• 2x + 10

• x^2 + 5

Open Ended

In each equation, what expression could be substituted for a so the equation is true for all values of x?

Fill in the Blanks

A perfect square is a number or expression that can be written as the square of a

.

Open Ended

How can you convert the expression 7x·7x into standard form (ax^2 + bx + c)?

Multiple Select

Which of the following are equivalent to a perfect square trinomial?

• (x+4)(x+4)

• x^2 + 8x + 16

• (x+4)^2

• x^2 + 16

Fill in the Blanks

Fill in the blank: The standard form of (x - 7)^2 is x^2 -

x + 49.

Multiple Choice

Which of the following is the correct standard form of (x + 1)^2?

• x^2 + 2x + 1

• x^2 + x + 1

• x^2 + 1

• x^2 + 2x

Fill in the Blanks

Write an equivalent expression of (x + n)^2 in standard form (ax^2 + bx + c).

Multiple Select

Which of the following expressions is a perfect square trinomial?

• x^2 + 6x + 9

• x^2 + 5x + 6

• x^2 - 16x + 64

• x^2 + 4x + 4

Open Ended

Why do you think the following expressions can be described as perfect squares? x^2 + 6x + 9 and x^2 - 16x + 64

Open Ended

How are the following expressions related in standard form to factored form?

Multiple Choice

What are the solutions to the equation (x - 6)^2 = 25 as solved by Noah?

• x = 11 or x = 1

• x = 6 or x = -6

• x = 5 or x = -5

• x = 25 or x = -25

Open Ended

Explain why, when solving (x - 6)^2 = 25, you set x - 6 equal to both 5 and -5.

Multiple Choice

Which of the following equations can be solved using the same method Noah used for (x - 6)^2 = 25?

• (y - 5)^2 = 49

• x^2 + 6x + 9 = 0

• x^2 - 10x + 25 = 0

• x^2 + bx + c = 0

Open Ended

Describe the relationship between the structure of the square diagrams and the factors of the quadratic expressions shown in Activity 3.

Multiple Choice

What is the factored form of the expression x^2 + 6x + 9?

• (x + 3)^2

• (x - 3)^2

• (x + 6)^2

• (x - 6)^2

Fill in the Blanks

Complete the blank: The process of finding the constant term to add in order to create a perfect square is called

the square.

Open Ended

Why is this quadratic expression not a perfect square trinomial, even though it contains a perfect square constant?

Open Ended

Compare Diego and Mai's methods for completing the square. What is one similarity and one difference in their approaches?

Multiple Choice

Which of the following is the correct order of steps for completing the square?

• Subtract c from both sides, divide b by 2 and square it, add to both sides, convert to factored form, take square root, split and solve for x

• Divide b by 2 and square it, subtract c from both sides, add to both sides, convert to factored form, take square root, split and solve for x

• Subtract c from both sides, add to both sides, divide b by 2 and square it, convert to factored form, take square root, split and solve for x

• Convert to factored form, subtract c from both sides, divide b by 2 and square it, add to both sides, take square root, split and solve for x

Multiple Choice

Which of the following quadratic equations can be solved by completing the square?

• x^2 + 6x + 8 = 0

• x^2 + 12x = 13

• 0 = x^2 - 10x + 21

• All of the above

Fill in the Blanks

Fill in the blank: In the equation x^2 + 12x = 13, after subtracting 13 from both sides, the next step in completing the square is to add

to both sides.

Multiple Select

Which of these quadratic expressions are perfect squares?

• x^2 + 4x + 8

• x^2 + 24x + 144

• x^2 + 6x + 16

• x^2 - 40x + 400

Open Ended

How confident do you feel about recognizing perfect-square quadratic expressions and using the method of completing the square to solve quadratic equations?

Fill in the Blanks

What is one method you learned today for solving quadratic equations?