To find the new equation of the graph, we start with the original function, which is given by:
y = x²
1. **Shifting Horizontally**: To shift the graph horizontally, we adjust the x-value of the function. A shift to the left by 5 units means we replace x with (x + 5). This transforms our equation into:
y = (x + 5)²
2. **Shifting Vertically**: Next, we will shift the graph vertically. A downward shift of 3 units implies we subtract 3 from the entire function. Therefore, we modify the equation as follows:
y = (x + 5)² – 3
So, after applying both shifts, the final equation representing the graph of y = x² shifted 3 units down and 5 units left is:
y = (x + 5)² – 3
This new equation accurately represents the transformed graph.