Hong Kong
Stage 4 - Stage 5

# Solve Applications Involving Parabolic Functions

## Interactive practice questions

The height $h$h, in metres, reached by a ball thrown in the air after $t$t seconds is given by the equation $h=10t-t^2$h=10tt2.

a

Fill in the following table of values for $h=10t-t^2$h=10tt2.

 $t$t $1$1 $2$2 $3$3 $4$4 $5$5 $6$6 $7$7 $8$8 $9$9 $10$10 $h$h $\editable{}$ $16$16 $\editable{}$ $24$24 $\editable{}$ $\editable{}$ $\editable{}$ $16$16 $\editable{}$ $0$0

b

Graph the relationship $h=10t-t^2$h=10tt2.

c

Determine the height of the ball after $5.5$5.5 seconds have elapsed.

d

What is the maximum height reached by the ball?

Easy
6min

A satellite dish is parabolic in shape, with a diameter of $8$8 metres. Incoming signals are reflected to one collection point, the focus of the parabola, marked as point $F$F on the diagram (not to scale). The focus is positioned such that the focal length is $4$4 metres.

Easy
5min

A parabolic antenna has a cross-section of width $16$16 m and depth of $2$2 m. All incoming signals reflect off the surface of the antenna and pass through the focus at $F$F. Note: Image is not to scale

Easy
4min

When an object is thrown into the air, its height above the ground is given by the equation $h=193+24s-s^2$h=193+24ss2, where $s$s is its horizontal distance from where it was thrown.

Easy
4min