Term 1 · Weeks 9–10 · Functions and Their Graphs

Challenge problem · non-routine

Challenge Non-routine

A ball thrown upward has height $h(t) = -5t^2 + 20t$ metres after $t$ seconds. What is the maximum height reached?

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Answer: 20 m

The graph is a parabola opening downward; the maximum is at the vertex $t = -\dfrac{b}{2a} = -\dfrac{20}{2(-5)} = 2$ .
$h(2) = -5(4) + 20(2) = -20 + 40 = 20$ m.

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