A ball is thrown upwards from the top of a building. Its height, $h$ metres, from the ground at ti

Question

A ball is thrown upwards from the top of a building.

Its height, $h$ metres, from the ground at time, $t$ seconds, is given by the equation $h=32+8t-4{{t}^{2}}$.

Some corresponding values of $h$ and $t$ are given in the table below.

$t$	$0$	$1$	$2$	$3$	$4$
$h$	$32$	$36$	$a$	$b$	$0$

Find the values of $a$ and $b$ in the table below.
Using a scale of 2 cm to 1 unit on the horizontal $x$-axis and 2 cm to 5 units on the
vertical $y$-axis, draw the graph of $h=32+8t-4{{t}^{2}}$ for $0\le t\le 4$.
Using your graph,
1. write down the height of the building,
2. find the maximum height of the ball from the ground,
3. determine at what time(s) is the ball 18 m from the ground.

Accepted Answer

(a) a = 32, b = 20; (c)(i) 32 m; (c)(ii) 36 m; (c)(iii) 3.1 s.

Quadratic Graphs in Real-Life Contexts