Question

The Diagram is in the comments!!
What is a scenario from science or engineering that this graph could model?
Not all quadratics are functions. What are some examples from science and engineering where a quadratic is used but is not a function?

Answer 1

This graph could represent the relative position of a projectile over time in a parabolic flight path. Since the y-intercept is greater than 0, the projectile is probably launched at a starting point higher than the ground, with the y-intercept being the initial height. A function is defined as a mathematical relationship between two variables in which the domain, or the "x" values do not repeat. However, in nature what we call an "x-value" very well may repeat. The path of nearly every known orbiting body in the universe, including moons, planets, and stars, follows the shape of an ellipse. However, when an ellipse is graphed it is not a function because to achieve its round, continuous shape the x-values have to be paired with a different y-value, and thus they repeat, causing the relation not to qualify as a function. Hope this helps :)