Ontario 10 Academic (MPM2D)
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Applications of maximization and minimization

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=12tt2.


Fill in the following table of values for $h=12t-t^2$h=12tt2

$t$t $1$1 $2$2 $3$3 $4$4 $5$5 $6$6 $7$7 $8$8 $9$9 $10$10
$h$h $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

Graph the relationship $h=12t-t^2$h=12tt2.

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Determine the height of the ball after $7.5$7.5 seconds have elapsed.


What is the maximum height reached by the ball?

Approx 6 minutes
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The sum of two integers is $80$80.

A rectangle is to be constructed with $80$80 metres of wire. The rectangle will have an area of $A=40x-x^2$A=40xx2, where $x$x is the length of one side of the rectangle.

The sum of two whole numbers is $24$24. Let one of the numbers be $x$x.



Solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology

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