University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

79

Pages:

7
Author:

recohatyh

Completing the Square uestion How can you complete the square for a quadratic expression? EXPLORATION: Using Algebra Tiles to Complete the Square Work with a partner. Use algebra tiles to complete the square for the expressioi:i x 2 + 6x. a. You can model x2 + 6x using one x2 -tile and six x-tiJes. Arrange the tiles in a square. Your arrangement will be incomplete in one of the corners. I b. iJ Jj � JJ How many I-tiles do you need to complete the square? '2 c. d. .2 Find the value of c so that the expression is a perfect square trinomial. + � 6x + .. c C '2- � ( ?(+ J Write the expression in part (c) as the square of a binomial. EXPLORATION: Drawing Conclusions Work with a partner. a. Use the method outlined in Exploration 1 to complete the table. Expression x2 tt- 2x-\-f(� x I:t 4�}+. -� x 2 + 8x :�c 2 x2 + lOx +··c ' Value of c needed to complete the square � --·Q 1 L ¼ �b...1 � �r -:v• 1 �2. � Expression written as a binomial squared [X +-1 ) ..1 (tt t-z_\"2. ( 7-· + <( )" �i..({:-- 11.r; :.(S'Y·� 'Z 5 b. Describe how you can solve the quadratic equation 1" • ... ·� r�-f sY� x 2 + 6x = 1 by;;f;;;l��i�;-;�-;�;�;�j -..� .. ... .. ..... ·•• .,..__� ., '- �(�') >< I, t� )( + t, :: J +· '\ r�llCd!��i ,.-- 1 1 _....,. ' (�+3\� ='lo x+ !> =- "!./to -) j -:> [x ; - !) 2:" JIO .J ,,, _ ,........,·;·• · ·-·· ··