NOTES: COMPLETING THE SQUARE
DAY 15
Textbook Chapter 4.7
OBJECTIVE:
Today you will learn about how to factor by completing the square!
SOLVING QUADRATIC EQUATIONS (Completing the Square A=1)
Step 1: Arrange the equation in the form Ax2 + Bx = C
Step 2: Determine what value for the third term
will make the trinomial a perfect square.
Step 3: Add that value to both sides.
Step 4: Simplify (write the trinomial as a binomial squared).
Step 5: Take the square root of both sides.
(remember the )
Step 6: Solve for x (often there are 2 solutions)
2.
Solve by completing the square.
x2 – 4x = 2x + 35
x2 + 10x – 3 = 0
SOLVING QUADRATIC EQUATIONS (Completing the Square A=1)
Step 1: Divide both sides by the GCF.
3x2 – 6x + 12 = 0
Step 2: Arrange the equation in the form Ax2 + Bx = C
Step 3: Determine what value for the third term
will make the trinomial a perfect square.
Then Add that value to both sides.
Step 5: Simplify (write the trinomial as a binomial squared).
Step 6: Take the square root of both sides.
(remember the )
Step 7: Solve for x (often there are 2 solutions)
CONVERT Standard Form to Vertex Form
Step 1: Factor out the coefficient (2) from the first two terms.
Step 2: Complete the square inside the parentheses.
Step 3: Distribute.
Step 4: Simplify.
y = 2x 2 + 8x − 5
PRACTICE: SOLVING EQUATIONS
DAY 15
BY COMPLETING THE SQUARE
1.
x2 + 10x = –23
2.
x2 + 2x = –17
3.
2x2 – 12x = –14
4.
4x2 + 16x = –12
CONVERT TO VERTEX FORM (by completing the square)
5.
y = 2x 2 + 16x − 7
6.
y = 3x 2 − 12x + 8
SOLVING QUADRATIC EQUATIONS: COMPLETING THE SQUARE
SOLUTIONS = X-INTERCEPTS = ROOTS = ZEROS
STANDARD
FORM
y = x2 – 2x – 8
y = x2 – 6x – 1
y = –2x2 – 12x – 10
CONVERT
TO VERTEX
FORM
(complete
the square)
Vertex: (
SOLVE
(find the
zeros)
Solve by
graphing
1
2
3
4
1
4
9
16
,
)
Vertex: (
,
)
Vertex: (
,
)
NAME: _____________________________________
DAY 15 DUE: _______
Solve the functions.
1.
y = x 2 − 20x + 100
2.
y = x 2 + 12x + 35
Solve the equations by completing the square.
3.
x2 + 2x = 9
4.
x2 – 4x = 2x + 35
5.
x2 + 20x + 104 = 0
6.
x2 – 17x + 200 = 13x – 43
7.
4x2 + 8x + 280 = 0
8.
6x2 + 300 = 84x
9.
Solve by completing the square.
10.
x2 + 2x = –17
11.
Convert to vertex form.
y = 3x 2 − 12x + 8
Solve by completing the square.
4x2 + 16x = –12
12.
Convert to vertex form.
y = x 2 + 12x + 35