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=10t−t2.
Fill in the following table of values for $h=10t-t^2$h=10t−t2.
| $t$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 |
Graph the relationship $h=10t-t^2$h=10t−t2.
Determine the height of the ball after $5.5$5.5 seconds have elapsed.
What is the maximum height reached by the ball?
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+24s−s2, where $s$s is its horizontal distance from where it was thrown.