A field-hockey ball must stay below waist height, approximately 1m, when shot; otherwise it is a dangerous ball. The function h(t) = -5t^2 + 10t where h (t) is in metres and t is in seconds, models the height of the ball. Has she shot a dangerous ball?

She shot a dangerous ball.

Step-by-step explanation:

According to the statement, we must prove that for all value . We know that height of the ball (), measured in metres, is represented by the following function:

(Eq. 1)

Where is the time, measured in seconds.

Which means that following inequation must be met:

From Algebra we know that product of either two positive numbers or two negative numbers is equal to a positive number, meaning that solution of inequation is:

and

By graphing the give

Which means that ball is a dangerous ball at .

Lastly, we present the graph of the function as attachment.

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