Answer:
We conclude that the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.
Hence, option D is true.
Please check the attached graph.
Step-by-step explanation:
Given the parent function
y = x²
Given the transformed function
y = (x - 12)²
Horizontal Translation:
The horizontal translation of y = x² is of the form
f(x-h)
so y = y = (x - 12)² means y = x² is shifted 12 right.
Vertical Translation:
y = x²
Then y = x² + b is a vertical translation of y = x²
if b > 0, then y = x² + b is the graph of y = x² 'b' units up.
if b < 0, then y = x² + b is the graph of y = x² 'b' units down.
Thus, y = x² + 3 means the graph y = x² is vertically shifted up by 2 units.
Please check the attached graph.
- The blue graph is representing the graph of y = x².
- The red graph is representing the graph of y = (x - 12)²+3
Therefore, the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.
Hence, option D is true.
