 New Zealand
Level 8 - NCEA Level 3

Solve Applications Involving Parabolic Functions

Interactive practice questions

The height $h$h, in meters, reached by a ball thrown in the air after $t$t seconds is given by the equation $h=12t-t^2$h=12tt2.

a

Fill in the following table of values for $h=12t-t^2$h=12tt2

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

Graph the relationship $h=12t-t^2$h=12tt2.

c

Determine the height of the ball after $7.5$7.5 seconds have elapsed.

d

What is the maximum height reached by the ball?

Easy
Approx 6 minutes

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.

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

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.

Outcomes

M8-1

Apply the geometry of conic sections

91573

Apply the geometry of conic sections in solving problems