Final answer:
A real-life situation that can be modeled by a quadratic equation with the given characteristics is the motion of a projectile, such as a ball being thrown into the air.
Step-by-step explanation:
A real-life situation that can be modeled by a quadratic equation with the given characteristics is the motion of a projectile. For example, consider a ball being thrown into the air. As it goes up, the height of the ball decreases at a slower rate compared to when it comes back down. This can be represented by a quadratic equation.
Let's say the equation is y = -x^2 + 5x + 10, where y represents the height of the ball and x represents time. The interval in which the function is decreasing is when x is in the range of 0 to 5, while the interval in which the function is increasing is when x is greater than 5.
Over the interval where the function is decreasing, the average rate of change is greater because the ball is losing height at a slower rate. On the other hand, over the interval where the function is increasing, the average rate of change is smaller because the ball is descending more rapidly.
Learn more about Modeling quadratic equations with real-life situations