What ste0ps transform the graph y = x^2 to y = 2(x + 2)^2 - 5?
A) Vertical Stretch by 5, shifted 5 units left and 2 down
B) Vertical Compress by 5, shifted 2 units left and 2 down
C) Vertical Compress by 2, shifted 2 units left and 5 down
D) Vertical Stretch by 2, shifted 2 units left and 5 down
The correct answer is D) Vertical Stretch by 2, shifted 2 units left and 5 down.
To transform the graph from y = x^2 to y = 2(x + 2)^2 - 5, the following steps are taken:
1) Vertical Stretch by 2: The coefficient 2 in front of the expression (x + 2)^2 indicates a vertical stretch by a factor of 2. This means the graph will be stretched vertically, making it narrower and taller.
2) Shifted 2 units left: The expression (x + 2)^2 indicates a horizontal shift to the left by 2 units. This means the graph will be moved horizontally to the left.
3) 5 down: The constant -5 at the end indicates a vertical shift downward by 5 units. This means the graph will be moved vertically downward.