Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3?
Answers
Answer:
Shifting the graph of equation 1 by 2 units left and 3 units up gives us the graph of equation 2
Step-by-step explanation:
Given that
y = x² ....(1
Our desired equation is
y = (x - 2)² + 3 .....(2
If we translate the graph of equation 1 by two units left we will have to replace x by x + 2. So, our equation would change the form to the following equation
y= (x + 2)² ....(3
If we translate the graph of equation 31 by three units up we will have to replace x by x + 3. So, our equation would change the form to the following equation
y = (x + 2)² + 3
This is our desired graph which has been obtained by shifting y = x² 2 units left, and then shifting it 3 units up in the coordinate plane.
So, our desired phrase is:
Shifting the graph of equation 1 by 2 units left and 3 units up gives us the graph of equation 2