If the parent function is f(x) = x2 and its transformed function is g(x) = 2(x − 1)2 + 2, how is the graph of g(x) transformed from the graph of its parent function?

stretch, shift along the y–axis, and shift along the x–axis
shift along the x–axis and the y–axis
reflection only
stretch along the y–axis and reflection through the origin

Option A is the correct choice.

Step-by-step explanation:  

We have been given a parent function and its transformed function is . We are asked to find the transformation rules used to function f(x) to get g(x).

First of all let us recall the translation rules.  

Upon looking at transformation rules we can see that the graph of g(x) is vertically stretched by a scale factor of 2. It is also shifted along the y-axis by 2 units upwards and along the x-axis by 1 unit to to the right.

Therefore, option A is the correct choice.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3