Completing the Square

Completing the Square

​Let’s rewrite equations to find the center and radius of a circle.

I can complete the square to find the center and radius of a circle.

​Learning Target

Fill in the Blanks

What value would need to be in the box in order for the expression to be a perfect square trinomial?

x² + 10x + ▢

Fill in the Blanks

What value would need to be in the box in order for the expression to be a perfect square trinomial?

x² - 16x + ▢

Fill in the Blanks

What value would need to be in the box in order for the expression to be a perfect square trinomial?

x² + 40x + ▢

Fill in the Blanks

What value would need to be in the box in order for the expression to be a perfect square trinomial?

x² + 5x + ▢

Completing Square and the equation of a circle

The technique of completing the square is used to turn an equation of a circle into the sum of a squared binomial and a number, to find the center and the radius of a circle

​Remember the center-radius form of the circle equation is in this format:

(x − h)² + (y − k)² = r²

Completing Square and the equation of a circle

Unfortunately, you may not always be given the equation of the circle in the form:

(x − h)² + (y − k)² = r²

​https://youtu.be/J3AwD0cdYC0

Open Ended

What did Elena do in the first step?

Open Ended

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

Open Ended

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

Open Ended

What did Elena do in step 3?

Open Ended

What are the center and radius of this circle?

Open Ended

Here is the equation of a circle: x² + y² - 2x + 4y - 4 = 0

Find the center and radius of the circle. Explain or show your reasoning.

Open Ended

Here is the equation of a circle: x² + y² + 12x + 2y + 12 = 0

Find the center and radius of the circle. Explain or show your reasoning.

I can complete the square to find the center and radius of a circle.

​Learning Target