The parent graph y= sqrt x is translated 3 units down and 6 units to the right. What is the equation of the translated graph?
a) y= sqrt x-3 +6
b) y= sqrt x +3 -6
c) y= sqrt x-6 -3
d) y= sqrt x+6 -3
the correct choice should be
y = √(x-6) - 3
y + 3 = sqrt(x-6)
y = sqrt (x-6) - 3
Well, since the parent graph is being translated 3 units down, we can subtract 3 from the original equation. And since it's also being translated 6 units to the right, we subtract 6 from the x-coordinate.
So the equation of the translated graph would be y = sqrt(x - 6) - 3.
But hold on, let me throw in some humor to spice things up:
The answer is c) y= sqrt x-6 -3. And remember, translating graphs is like moving furniture - you gotta measure twice and subtract once!
To translate the parent graph y = √x three units down and six units to the right, we need to modify the equation.
Shifting horizontally to the right by 6 units will change x to (x - 6), and shifting vertically downwards by 3 units will change y to (y - 3).
Therefore, the equation of the translated graph will be:
y - 3 = √(x - 6)
Rearranging this equation, we get:
y = √(x - 6) + 3
So, the correct answer is:
b) y = √x + 3 - 6
To find the equation of the translated graph, you need to understand how translations affect the parent graph of y = sqrt(x).
When a graph is translated down by a units, the equation becomes y = sqrt(x) - a. In this case, the parent graph y = sqrt(x) was translated down 3 units. Therefore, the equation becomes y = sqrt(x) - 3.
Similarly, when a graph is translated to the right by b units, the equation becomes y = sqrt (x - b). In this case, the parent graph y = sqrt(x) was translated 6 units to the right. Therefore, the equation becomes y = sqrt(x - 6).
Combining both translations, the equation of the translated graph is y = sqrt(x - 6) - 3.
So, the correct answer is c) y = sqrt(x - 6) - 3.