Quadratic Equations

Hong Kong

Stage 4 - Stage 5

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`=10`t`−`t`2.

a

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

$t$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`=10`t`−`t`2.

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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`=40`x`−`x`2, 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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