Question

Without graphing, describe the transformations of each parabola or absolute value function 2) y =(x + 4) + 4 3) y=-2(x+4)² + 4 Fo 4 y = |x-31+3 5) y= 2(x - 1)2 + 4 T) y = -3/x-21 v- +11+3 = 2/x - 3/+4 9) y = 2|x1 + +1Please, solve for cases 3 and 4 only.

Answer 1

Solving for Case 3:

y = -2(x + 4)^2 + 4

We have that the parent function is:

y = x^2

This parabola has a transformation as follows:

1. It has a vertical shift of four units upward.

2. It moves four units to the left (a horizontal shift to left in four units.)

3. It is vertically stretched by 2 (its y-coordinates) and it is followed by a reflection across the x-axis (it was multiplied by -2.) In the latter, the parabola is open downward.

(In this case last case we have (x, y) ---> (x, -2y).)

Solving for the Case 4:

| x - 3 | + 3

In this case, the parent function is:

y = | x |

This function has a transformation as follows:

1. It has a horizontal shift to the right of three units.

2. It has a vertical shift upwards of three units.