L6.6 - Completing the Square

For each expression, what value would need to be in the box in order for the expression to be a perfect square trinomial? 1. x² + 10x + ▢

2. x² - 16x + ▢

3. x² + 40x + ▢

4. x² + 5x + ▢

Here is the equation of a circle: x² + y² - 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: x² - 6x + y² - 20y  = -105 Step 2: x² - 6x + 9 + y² - 20y + 100 = -105 + 9 + 100 Step 3: x² - 6x + 9 + y² - 20y + 100 = 4 1. What did Elena do in the first step?

2. Why did Elena add 9 and 100 to the left side of the equation in Step 2?

3. Why did Elena add 9 and 100 to the right side of the equation in Step 2?

4. What should Elena do next?

5. What are the center and radius of this circle?

Here is the equation of a circle: x² + y² - 2x + 4y - 4 = 0 1. Find the center and radius of the circle. Explain or show your reasoning.

1. x² + y² - 24y + 143 = 0 2. (x + 35)² + (y - 50)² = 19 What makes each of these different from the ones you’ve already studied?

Find the center and radius each.

Here is the equation of a circle: x² + y² + 12x + 2y + 12 = 0 Find the center and radius of the circle.