# Completing the Square

ID: dafim-kidim Illustrative Mathematics, CC BY 4.0
Subject: Geometry
Standards: HSA-SSE.B.3HSG-GPE.A.1

15 questions

# Completing the Square

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##### Fill in the Box

For each expression, what value would need to be in the box in order for the expression to be a perfect square trinomial?

1) ﻿$x^2 + 10x + \boxed{\phantom{3}}$﻿

2) ﻿$x^2 - 16x + \boxed{\phantom{3}}$﻿

3) ﻿$x^2 + 40x + \boxed{\phantom{3}}$﻿

4) ﻿$x^2 + 5x + \boxed{\phantom{3}}$﻿

##### Complete the Process

Here is the equation of a circle: ﻿$x^2 + y^2 - 6x - 20y + 105 = 0$﻿.

Elena wants to find the center and radius of the circle. Here is what she’s done so far.

Step 1: ﻿$x^2 - 6x + y^2 - 20y = -105$﻿

Step 2: ﻿$x^2 - 6x + 9 + y^2 - 20y + 100 = -105 + 9 + 100$﻿

Step 3: ﻿$x^2 - 6x + 9 + y^2 - 20y + 100 = 4$﻿

5) What did Elena do in the first step?

6) Why did Elena add 9 and 100 to the ﻿$\textit{left}$﻿ side of the equation in Step 2?

7) Why did Elena add 9 and 100 to the ﻿$\textit{right}$﻿ side of the equation in Step 2?

8) What should Elena do next?

9) What is the center of this circle?

10) What is the radius of this circle?

11) Draw a graph of the circle. Here is the equation of a circle: ﻿$x^2 + y^2 - 2x + 4y - 4 = 0$﻿. 