Maybe an oversimplification but ELI5 hopefully. Think of throwing a ball up into the air. Starts heading up eventually stops at the top, and starts heading down until it hits the ground and stops again.
Quadratic would help answer questions like:
When (as a time factor) will the ball be 2 meters above the ground? Well at one point when it’s heading up it will hit 2 meters, and another when it’s heading down, but at different times.
Or, when will the ball have 0 speed? Realistically at the top of the arc and when it hits the ground.
Or, when will the ball be travelling 0.5 meters per second, once as it’s slowing down but heading up, and once when it’s speeding up and heading down.
Rinse and repeat for parabolic activities while solving for singular points.
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