In h(t) = -16 t^2 + v0 t + h0, at what time t is the maximum height reached?

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Study for the Algebra 1 Honors End-of-Course Test. Study with flashcards and multiple-choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

In h(t) = -16 t^2 + v0 t + h0, at what time t is the maximum height reached?

Explanation:
Height as a function of time is a downward-opening parabola, so its highest point is at the vertex. For a quadratic ax^2 + bx + c, the time at the vertex is t = -b/(2a). Here a = -16 and b = v0, giving t = -v0/(2(-16)) = v0/32. So the maximum height occurs at t = v0/32. This also matches the idea that the velocity dh/dt = -32t + v0 becomes zero at that moment, marking the transition from rising to falling.

Height as a function of time is a downward-opening parabola, so its highest point is at the vertex. For a quadratic ax^2 + bx + c, the time at the vertex is t = -b/(2a). Here a = -16 and b = v0, giving t = -v0/(2(-16)) = v0/32. So the maximum height occurs at t = v0/32. This also matches the idea that the velocity dh/dt = -32t + v0 becomes zero at that moment, marking the transition from rising to falling.

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