√3-(x-6)^2 + 15
What are the transformations in this? Confused by the three.
(x -3)^2 + (y - 7)^2 =.25
Is there a transformation on the radius?
Or just the center?
I do not know what you are talking about with the first one. It is nott an equation
the second one is a circle with center at (3,7) and radius of 0.50
yes, so what are the actual transformations of the circle ? I know that it moves up 7 units and to the right 3. Does the radius/diameter of it have any separate transformation? And shouldn't the radius be .25/2? Not multiplied by 2? How is it not an equation? I was wondering about is it a horizontal compression of 3 or is it a shift?
no, the radius is the radius
it is r^2 = 0.25
so
r = 0.50
(x-k)^2 + (y-h)^2 = r^2
center at (h,k)
radius of r
NOT multiplied by 2
radius SQUARED on the right
r times r
ok, so the radius is separate from the transformations. They got to the radius squared by .5^2.
To identify the transformations in an equation, you need to understand what each component represents. Let's break it down for each of the given equations:
1. √3-(x-6)^2 + 15:
- √3: This term represents a vertical shift of the graph by three units upwards.
- (x-6)^2: This term represents a horizontal translation of the graph six units to the right.
- +15: This term represents a vertical shift of the graph by 15 units upwards.
2. (x -3)^2 + (y - 7)^2 = .25:
- (x - 3)^2: This term represents a horizontal translation of the graph three units to the right.
- (y - 7)^2: This term represents a vertical translation of the graph seven units upwards.
- = .25: This term represents the radius of the graph. The equation specifies that the distance between any point on the graph and the center is 0.25 units.
In summary, for the first equation, there is a vertical shift, a horizontal translation, and another vertical shift. For the second equation, there are only translations (horizontal and vertical) and a specified radius; no transformation applies to the radius itself.
Remember that transformations describe changes to the graph's position, shape, or size without altering the essential nature of the function.