A ball is thrown in the air so that $t$ seconds after it is thrown, its height $h$ metre above its starting point is given by the polynomial $h = 25t - 5t^2$.

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Observe the graph of the poly

Question

A ball is thrown in the air so that $t$ seconds after it is thrown, its height $h$ metre above its starting point is given by the polynomial $h = 25t - 5t^2$.

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Observe the graph of the polynomial and answer the following questions:
(i) Write zeroes of the given polynomial.
(ii) Find the maximum height achieved by ball.
(iii) (b) Find the two different values of $t$ when the height of the ball was $20$ m.

Accepted Answer

Step 1: (i) Zeroes of the polynomial are $0$ and $5$.
Step 2: (ii) Maximum height $= 25 	imes \frac{5}{2} - 5 	imes \left(\frac{5}{2}ight)^2 = \frac{125}{4} = 31.25$ m
Step 3: (iii)(b) $-5t^2 + 25t = 20 \Rightarrow t^2 - 5t + 4 = 0 \Rightarrow (t - 4)(t - 1) = 0$
Step 4: $t = 4$ and $t = 1$

Question

Solution