Answer:The given equations are two different forms of the same quadratic function. In particular, they represent parabolas that have been shifted in the x-y plane.
The general form of a quadratic equation is y = ax^2 + bx + c, where a, b and c are constants. To convert from the first form y=(x+3)^2+4 to the second form y=(x+1)^2+6, we need to complete the square by manipulating both sides of the equation:
y = (x + 3)^2 + 4 y - 4 = (x + 3)^2 (y - 4) / a = x^2 + bx / a // Here we divide both sides by "a", where "a" is equal to one.
Now let's compare this with our new equation:
y= (x+1)²+6 y-6= (x+1)²
Comparing these two equations gives us:
(y - 4) / a = x^2 + bx / a --> (y-6)/1=x²+(0)x/1
We can see that b must be zero for these two functions to be equivalent. This means that there is no horizontal shift between them; they share the same vertex at (-3,-4)=(−1,−6).
However, there is vertical shift between them: The vertex has been moved up by an amount of (+6 −(−4))=10 units.
Therefore, using vector notation T<h,k>, where h represents horizontal translation and k represents vertical translation or shifting , we can say that transformation from first function to second function involves T<0,+10>.
So our answer should be D. T<2,2>.
Explanation: