To find the time at which maximum height is reached, use the vertex formula $ t = -\frac{b}{2a} $ for the quadratic equation $ h(t) = -5t^2 + 20t + 10 $.

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# How to Find the Time at Which Maximum Height Is Reached Using the Vertex Formula When analyzing the motion of an object under gravity, such as a ball thrown into the air, one key question is: At what time does the object reach its maximum height? For quadratic equations that model height over time, the answer lies in finding the vertex of the parabola represented by the equation. This allows us to determine the exact moment of peak elevation without graphing the function. ## Understanding the Quadratic Model In physics and mathematics, projectile motion is often described by a quadratic equation of the form: