To fit the parabola to the top-left fountain spurt, apply horizontal and vertical translations, stretch or compress vertically, and potentially reflect the parabola to match the spurt's shape and trajectory.
To make the parabola fit the top-left fountain spurt, several transformations need to be applied. The standard form of a parabola is \(y = ax^2 + bx + c\). The transformations required involve adjusting the coefficients and introducing translations.
1. **Translation:**
The entire parabola needs to be shifted horizontally and vertically. If the vertex of the standard parabola is at (0,0), the new vertex should match the coordinates of the top-left fountain spurt.
2. **Stretch/Compression:**
Adjust the coefficient \(a\) to control the vertical stretch or compression of the parabola. This ensures that the shape of the parabola aligns with the water trajectory.
3. **Reflection:**
Depending on the orientation of the fountain spurt, a reflection may be needed to match the upward or downward direction of the water.
4. **Translation in x-direction:**
Fine-tune the position of the parabola horizontally to align it precisely with the spurt's trajectory.
The sequence of transformations will depend on the specific details of the fountain spurt's shape and location. Experimenting with translations, stretching, and reflections will help achieve the desired fit.