4.6 Completing the Square
Name: ____________________
Objectives: Students will be able to solve quadratic functions by completing
the square. Students will be able to rewrite functions by completing the
square.
Factor: x2 + 8x + 16
Examples: Find the value of c that makes the expression a
perfect square. Then write the expression as the square of a
binomial.
2.) x2 - 13x + c
1.) x2 + 12x + c
Nov 7­9:35 AM
Steps to completing the square:
1.) Put the constant on the right hand side.
2.) Make sure the coefficient on x2 is 1. If not, divide through to make it 1.
3.) Take half of the coefficient on x, square it and add it to both sides.
4.) Factor the left hand side.
5.) Take the square root of each side and solve for x.
Solve by completing the square.
3.) x2 + 4x = 10
Nov 7­9:36 AM
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4.) x2 - 6x - 3 = 0
5.) 2x2 + 16x + 12 = 0
Nov 7­9:37 AM
6.) 7x2 + 28x + 56 = 0
7.) 3x2 - 4x = 2
Nov 7­9:39 AM
2
4.6 Homework
Name: _______________
Examples: Find the value of c that makes the expression a perfect
square. Then write the expression as the square of a binomial.
1.) x2 + 10x + c
2.) x2 - 20x + c
3.) x2 - 7x + c
4.) x2 + 9x + c
Nov 10­2:32 PM
Solve by completing the square.
5.) x2 - 12x + 7 = 0
6.) x2 + 4x + 2 = 0
Oct 18­9:53 AM
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7.) x2 + 5x = 3
8.) 3x2 - 12x + 6 = 0
Oct 18­9:53 AM
Make sure to combine like terms first. Then complete the
square.
9.) x2 + 2 = 6x + 4
10.) 2x2 + 2x - 5 = x2
Oct 18­9:56 AM
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