Quadratic Equations
Applications of maximisation and minimisation
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=12t−t2.
a
Fill in the following table of values for $h=12t-t^2$h=12t−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 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
b
Graph the relationship $h=12t-t^2$h=12t−t2.
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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
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Outcomes
NA6-4
Find optimal solutions, using numerical approaches
91028
Investigate relationships between tables, equations and graphs