Question

How is the graph of y =(x-1)2 - 3 transformed to produce the graph of y = 5(X+4)??

The graph is translated left 5 units, compressed vertically by a factor of 5, and translated up 3 units.
The graph is stretched vertically by a factor of 3, translated left 5 units, and translated up 3 units
The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units
The graph is stretched horizontally by a factor of 2, translated left 5 units, and translated down 3 units

Answer 1

A.

Explanation:

The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.

Answer 2

The graph is translated left 5 units, compressed vertically by a factor of 5, and translated up 3 units.

Explanation:

The initial function is

`y=(x-1)^(2) -3`

The transformed function is

`y=5(x+4)^(2)`

Notice that the first function represents a parabola with vertex at (1, -3), and the secong function represents a parabola with vertex at (-4, 0). That means the function was shifted three units up and 5 units to the left. Additionally, the function was compressed by a scale factor of 5, because that's the coffecient of the quadratic term.

Therefore, the right answer is the first choice.