IM Alg1.7.12 Lesson: Completing the Square (Part 1)
[size=150]Select [b]all [/b]expressions that are perfect squares. Explain how you know.[/size][br][br][math](x+5)(5+x)[/math]
[math](x+5)(x-5)[/math]
[math](x-3)^2[/math]
[math]x-3^2[/math]
[math]x^2+8x+16[/math]
[math]x^2+10x+20[/math]
Complete the table so that each row has equivalent expressions that are perfect squares.
[size=150]One technique for solving quadratic equations is called [b]completing the square[/b][i].[/i] Here are two examples of how Diego and Mai completed the square to solve the same equation. [br][br][table][tr][td]Diego:[/td][td]Mai:[/td][/tr][tr][td][math]\displaystyle \begin {align} x^2+10x+9 &=0 \\x^2+10x &= \text-9 \\ x^2+10x+25 &=\text-9 + 25\\x^2+10x+25 &=16 \\ (x+5)^2 &=16\\ x+5=4 \quad & \text{or} \quad x+5=\text-4\\ x=\text-1 \quad & \text{or} \quad x=\text-9 \end{align}[/math][/td][td][math]\begin {align} x^2 + 10x + 9 &= 0\\ x^2 + 10x + 9 + 16 &= 16\\ x^2+10x+25 &=16\\ (x+5)^2&=16\\ x+5=4 \quad & \text{or} \quad x+5=\text-4\\ x=\text-1 \quad & \text{or} \quad x=\text-9 \end {align}[/math][br][/td][/tr][/table][br][/size][size=150][br]Study the worked examples. Then, try solving these equations by completing the square:[br][/size][br][math]x^2+6x+8=0[/math]
[math]x^2+12x=13[/math]
[math]0=x^2-10x+21[/math]
[math]x^2-2x+3=83[/math]
[math]x^2+40=14x[/math]
Here is a diagram made of a square and two congruent rectangles.
[size=150]Its total area is [math]x^2+35x[/math] square units.[br][br][/size]What is the length of the unlabeled side of each of the two rectangles?[br]
If we add lines to make the figure a square, what is the area of the entire figure?[br]
How is the process of finding the area of the entire figure like the process of building perfect squares for expressions like [math]x^2+bx[/math]?
IM Alg1.7.12 Practice: Completing the Square (Part 1)
Add the number that would make the expression a perfect square. Next, write an equivalent expression in factored form.
[math]x^2-6x[/math]
[math]x^2+2x[/math]
[math]x^2+14x[/math]
[math]x^2-4x[/math]
[math]x^2+24x[/math]
[size=150]Mai is solving the equation [math]x^2+12x=13[/math]. She writes:[br][size=100][math]\displaystyle \begin{align} x^2 + 12x &= 13\\ (x + 6)^2 &= 49\\ x &= 1 \text { or } x = \text- 13\\ \end{align}\\[/math][/size][br][br]Jada looks at Mai’s work and is confused. She doesn’t see how Mai got her answer.[/size][br][br]Complete Mai’s missing steps to help Jada see how Mai solved the equation.[br]
Solve each equation by completing the square.
[math]x^2-6x+5=12[/math]
[math]11=x^2+4x-1[/math]
[math]x^2-2x=8[/math]
[math]x^2-18x+60=\text{-}21[/math]
Rewrite each expression in standard form.
[math](x+3)(x-3)[/math]
[math](7+x)(x-7)[/math]
[math](2x-5)(2x+5)[/math]
[math]\left(x+\frac{1}{8}\right)\left(x-\frac{1}{8}\right)[/math]
[size=150]To find the product [math]203\cdot197[/math] without a calculator, Priya wrote [math](200+3)(200-3)[/math]. Very quickly, and without writing anything else, she arrived at 39,991. [/size][size=150]Explain how writing the two factors as a sum and a difference may have helped Priya.[/size]
[size=150]A basketball is dropped from the roof of a building and its height in feet is modeled by the function [math]h[/math].[br][br]Here is a graph representing [math]h[/math].[/size][br][img]data:image/png;base64,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[/img][br]Select [b]all [/b]the true statements about this situation.
[size=150]A group of students are guessing the number of paper clips in a small box.[br][br]The guesses and the guessing errors are plotted on a coordinate plane.[br][img]data:image/png;base64,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[/img][br]What is the actual number of paper clips in the box?[/size]