Question

For the function y= ₋2[(x-1)²/2], describe the transformation from the parent function y = x².

a. Reflection in the x-axis
b. Vertical compression by a factor of 2
c. Horizontal shift to the right by 1 unit
d. Vertical shift downward by 2 units

Answer 1

The function y = ₋2[(x-1)²/2] is a transformation of the parent function y = x² involving reflection, compression, and shifts.

Step-by-step explanation:

The function y = ₋2[(x-1)²/2] can be described as a transformation of the parent function y = x² as follows:

1. Reflection in the x-axis: The negative coefficient ₋2 reflects the graph of the parent function in the x-axis. This means that all positive y-values become negative and vice versa.
2. Vertical compression by a factor of 2: The squared term (x-1)² in the numerator compresses the graph vertically by a factor of 2. This means that the y-values of the graph are halved compared to the parent function.
3. Horizontal shift to the right by 1 unit: The term (x-1) shifts the graph 1 unit to the right. This means that the vertex of the parabola is shifted from (0,0) to (1,0).
4. Vertical shift downward by 2 units: The negative coefficient ₋2 in the function causes a vertical shift downward by 2 units. This means that the entire graph is shifted downward by 2 units.