Final answer:
The function y = -5(x-2)² + 3 undergoes several transformations compared to the parent graph y = x²: a horizontal shift right by 2 units, a vertical stretch by a factor of 5 combined with reflection across the x-axis, and a vertical shift upward by 3 units.
Step-by-step explanation:
The quadratic function given by y = -5(x-2)² + 3 represents a transformation of the parent function y = x². The transformations that occur are:
- Horizontal shift: The term (x-2) within the quadratic indicates a horizontal shift of the parent graph 2 units to the right.
- Vertical stretch and reflection: The coefficient -5 in front of the quadratic causes the graph to be vertically stretched by a factor of 5 and reflected across the x-axis.
- Vertical shift: The +3 at the end of the equation represents an upward vertical shift of the graph by 3 units.
So, the graph of y = -5(x-2)² + 3 can be obtained by taking the graph of y = x², shifting it 2 units to the right, reflecting it vertically, stretching it by a factor of 5, and shifting it up by 3 units.