IM Geo.6.6 Practice: Completing the Square

Suppose a classmate missed the lessons on completing the square to find the center and radius of a circle. Explain the process to them. If it helps, use a problem you’ve already done as an example.

Match each expression with the value needed in the box in order for the expression to be a perfect square trinomial.

[math]x^2 -8x+\boxed{ }[/math]

100 16 20.25 64

[math]x^2 +20x+\boxed{ }[/math]

100 20.25 64 16

[math]x^2 -16x+\boxed{ }[/math]

16 20.25 64 100

[math]x^2 +9x+\boxed{ }[/math]

64 20.25 16 100

[size=150]Find the center and radius of the circle represented by the equation [math]x^2+y^2+4x-10y+20=0[/math][/size].

[size=150] Select[b] all[/b] the expressions that can be factored into a squared binomial.[/size]

[math]x^2-10x+25[/math] [math]y^2+2y+1[/math] [math]w^2+5w+\frac{25}{4}[/math] [math]x^2+10x+25[/math] [math]w^2+20w+40[/math] [math]y^2-10y+5[/math]

[size=150]An equation of a circle is given by [math]\left(x+3\right)^2+\left(y-9\right)^2=5^2[/math]. Apply the distributive property to the squared binomials and rearrange the equation so that one side is 0.[/size]

Graph the circle (x+1)²+(y-3)²=16.

Find the distance from the center of the circle to each point on the list.

[math]\left(2,1\right)[/math]

[math]\left(4,1\right)[/math]

[math]\left(3,3\right)[/math]

What do these distances tell you about whether each point is inside, on, or outside the circle?[br]

[size=150]The triangle whose vertices are [math]\left(3,-1\right),\left(2,4\right)[/math] and [math]\left(5,1\right)[/math] is transformed by the rule [math]\left(x,y\right)\rightarrow\left(2x,5y\right)[/math]. Is the image similar or congruent to the original figure?[/size]

The image is similar but not congruent to the original triangle. The image is neither similar nor congruent to the original triangle. The image is congruent to the original triangle.

A cube has side length 3 inches. A sphere has a radius of 3 inches.

Before doing any calculations, predict which solid has greater surface area to volume ratio.[br]

Calculate the surface area, volume, and surface area to volume ratio for each solid.[br]

IM Geo.6.6 Practice: Completing the Square

Match each expression with the value needed in the box in order for the expression to be a perfect square trinomial.

Graph the circle (x+1)²+(y-3)²=16.

Find the distance from the center of the circle to each point on the list.

A cube has side length 3 inches. A sphere has a radius of 3 inches.

Information: IM Geo.6.6 Practice: Completing the Square