Completing The Square Warm-Up!


What is the formula used to find C to complete the square?

a) (b/2) 2

b) (2/b) 2

c) 2b 2

d) 1/2b


Below type in the missing term to make it a complete square (no decimals).


X 2 + 6x + ___



X 2 + x + ___


What is X 2 +6x + 8 in Vertex Form?

a) (x+3) 2 +9

b) (x+9) 2 +8

c) (x+3) 2 -1

d) (x+3) 2 -9

What are the zeros for the previous equation?

a) x = -2, x = 4

b) x = -3, x = 1

c) x = 2, x = 4

d) x = -2, x = -4



X 2 +6x + 8
Put 8 on the outside (X 2 +6x___) +8
Find the C term to make a perfect square (6/2) 2 = 9
(X 2 +6x +9) +8
Since we added nine on the inside we must subtract nine from the outside so the action cancels out
(X 2 +6x +9) +8 -9 (+9-9 = 0)
(X 2 +6x +9) -1
Factor what is inside the parentheses into a perfect square
(X+3) 2 -1 = 0
Now it is in vertex form! To find the zeros we must get X alone by first adding one
(X+3) 2 = 1
Now since we added one to both sides we can square root both sides to cancel out the square
(X+3) 2 = 1
we are now left with X + 3 =+/- 1 because the square root of one can be +1 or -1
To get X completely alone we need to subtract three from both sides, leaving us with
x = +/- 1 -3
x = 1 - 3 = -2, x = -1 - 3 = -4