Respuesta :
Answer:
y=-(x+2)^2 -6
Step-by-step explanation:
y=a(x-h)^2 + 6
a=-1
h=-2
k=-6
The vertex of y=x^2 is on (0,0)
When you shift an equation down, and when you shift an equation left you are basically subtracting from the y and x components respectively, so:
(0-2,0-6) = (-2,-6) = (h,k)
Or, you can just remember that a positive k (or y) , is above the origin and a negative k is below the origin.
H (or x) is the opposite. Positive h is to the left and negative h is to the right.
The function of the graph of y=√x after the graph is shifted down 6 units, reflected about the x-axis, and finally shifted left 2 units transformations is y= - ((√x+2)-6). This is obtained by using rules of transformation of linear function.
What are the Rules of Transformation of Linear Function?
Rules of transformation of linear function are
- f(x)+b - function is shifted b units upward
- f(x)-b - function is shifted b units downward
- f(x+b) - function is shifted b units to the left
- f(x-b) - function is shifted b units to the right
- -f(x) - function is reflected over x-axis
- f(-x) - function is reflected over y-axis
Find the function required:
Given that the function is y=√x.
- First the graph is shifted down 6 units
By the transformation we can rewrite the function in f(x)-b form;
that is ⇒ y = ((√x)-6)
- Next the graph is reflected about the x-axis
By the transformation we can rewrite the function in -f(x) form;
that is ⇒  y = - ((√x)-6)
- Finally the graph is shifted left 2 units
By the transformation we can rewrite the function in f(x+b) form;
that is ⇒ y= - ((√x+2)-6)
This is the required function.
Hence the function of the graph of y=√x after the graph is shifted down 6 units, reflected about the x-axis, and finally shifted left 2 units transformations is y= - ((√x+2)-6).
Learn more about transformation rules here:
brainly.com/question/51939790
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