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`=12`t`−`t`2.

a

Fill in the following table of values for $h=12t-t^2$`h`=12`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 |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

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

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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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Apply the geometry of conic sections

Apply the geometry of conic sections in solving problems