Quadratic Equations
New Zealand
Level 7 - NCEA Level 2
Applications of maximisation and minimisation
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.
a
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 |
b
Graph the relationship $h=10t-t^2$h=10t−t2.
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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
The sum of two integers is $80$80.
Easy
3min
A rectangle is to be constructed with $80$80 metres of wire. The rectangle will have an area of $A=40x-x^2$A=40x−x2, where $x$x is the length of one side of the rectangle.
Easy
5min
The sum of two whole numbers is $24$24. Let one of the numbers be $x$x.
Easy
4min
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