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One real-world application of quadratic functions is to describe an object's height in projectile motion. A ball thrown upward can be characterized by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the starting height (Stewart, 2016). The function's vertex represents the ball's highest height and time of arrival. The x-intercepts tell when the ball is launched and returned to the ground. The y-intercept reflects the ball's original height. Understanding these characteristics is critical in disciplines such as physics, engineering, and sports science.
Answer (2)
Quadratic functions model projectile motion, allowing for the prediction of an object's height over time. Key features include the vertex (maximum height), x-intercepts (ground level times), and y-intercept (initial height). This understanding is important in physics, engineering, and sports science.
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One real-world application of quadratic functions is modeling the height of an object in projectile motion. For example, the motion of a ball thrown upward can be described by the equation , where represents the initial velocity and is the initial height (Stewart, 2016). In this context, the vertex of the parabola corresponds to the ball's maximum height and the time at which it is reached. The x-intercepts indicate the times when the ball is at ground level—both at launch (if starting from ground level) and when it returns to the ground. The y-intercept reflects the initial height from which the ball was thrown. Understanding these features is essential in fields such as physics, engineering, and sports science, where precise modeling of motion is critical. ;
