Write a function for the graph described as a transformation of y=x^2
y=x^2 experiences a vertical stretch of factor 2 and then a shift right of 3 units.
how about
y = 2x^2 + 3
I think I prefer
y = 2(x-3)^2
To write a function for the graph described as a transformation of y=x^2, we need to apply the given transformations: a vertical stretch of factor 2 and a shift right of 3 units.
Let's break down the transformations step by step:
1. Vertical Stretch of Factor 2:
To vertically stretch a graph by a factor of 2, we multiply the original function by the scaling factor. In this case, multiplying y=x^2 by 2 gives us y=2x^2.
2. Shift Right by 3 Units:
To shift a graph to the right, we subtract the desired amount from the variable (x). In this case, we need to shift the graph 3 units to the right. Therefore, we replace x with (x - 3) in the function from the previous step, resulting in y=2(x - 3)^2.
Putting it all together, the function for the transformed graph is:
y = 2(x - 3)^2.
This function represents a vertical stretch of factor 2 and a shift right of 3 units from the original graph y = x^2.