Interpret a quadratic height model
Use a quadratic height model h(t) = -5t^2 + vt + h0 to find a maximum height or the time an object lands. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
A basketball is thrown from the ground. Its height h, in metres, after t seconds is modeled by the equation shown. What is the maximum height it reaches?
h(t) = −5t2 + 10t
Answer: 5
See one solved, step by step
A model rocket is launched from the ground. Its height h, in metres, after t seconds is modeled by the equation shown. How many seconds until it lands (returns to the ground)?
h(t) = −5t2 + 50t
📘 Worked solution
1h(t) = −5t2 + 50t -> −5t(t - 10) = 0Factor out -5t — this is possible because it's launched from the ground, so there's no constant term.
2t = 0 or t = 10A product is zero only when one of the factors is zero.
3t = 0 is the launch moment, so the model rocket lands at t = 10 s.The parabola is symmetric about its vertex at t = 5, so the two zero-height times are equally spaced around it.
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