# Worksheet: Completing the Square

In this worksheet, we will practice completing the square to factor quadratic expressions.

Q1:

Given that , what are the values of and ?

• A,
• B,
• C,
• D,
• E,

Q2:

Given that , what are the values of and ?

• A,
• B,
• C,
• D,
• E,

Q3:

Given that , what are the values of and ?

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q4:

What is the vertex form of the function ?

• A
• B
• C
• D
• E

Q5:

In completing the square for quadratic function , you arrive at the expression . What is the value of ?

Q6:

Given that , what are the values of , , and ?

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q7:

What is the vertex form of the function ?

• A
• B
• C
• D
• E

Q8:

Write the equation in the form .

• A
• B
• C
• D
• E

Q9:

Write the equation in the form .

• A
• B
• C
• D
• E

Q10:

Write the equation in the form .

• A
• B
• C
• D
• E

Q11:

Write the equation in the form .

• A
• B
• C
• D
• E

Q12:

Write the equation in the form .

• A
• B
• C
• D

Q13:

Write the equation in the form .

• A
• B
• C
• D
• E

Q14:

Write the equation in the form .

• A
• B
• C
• D
• E

Q15:

Write the equation in the form .

• A
• B
• C
• D
• E

Q16:

Write the equation in the form .

• A
• B
• C
• D
• E

Q17:

Write the equation , where , in the form .

• A
• B
• C
• D
• E

Q18:

Which of the following equations can be transformed into the equation by expanding, rearranging, and multiplying by a scalar?

• A
• B
• C
• D
• E

Q19:

Given that can be written in the form , find the value of .

• A
• B
• C
• D
• E3

Q20:

Find the values of for which the equation is satisfied by only one value of .

• A
• B
• C
• D
• E

Q21:

Given that and , find the value of .

Q22:

Which of the following equations can be expanded and rearranged to ?

• A
• B
• C
• D
• E

Q23:

By writing in the form , determine when the equation has no real roots.

• Awhen
• Bwhen or
• Cwhen
• Dwhen
• Ewhen

Q24:

Factorize fully .

• A
• B
• C
• D
• E

Q25:

Factorize fully .

• A
• B
• C
• D
• E