Quadratic Relations

The Gateway Arch in St. Louis, Missouri, is $190$190 m tall.

We can model the behaviour of objects falling from the arch using Galileo's formula for falling objects: $d=16t^2$`d`=16`t`2, where $d$`d` is distance fallen in metres and $t$`t` is time in seconds since the object was dropped. The graph of this relationship is drawn here.

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What does the point at $\left(0,0\right)$(0,0) represent?

The height of the arch.

A

The position of the object after it has fallen to to the ground.

B

The initial distance fallen by the object.

C

Easy

< 1min

The sum of the series $1+2+3+\ldots+n$1+2+3+…+`n` is given by the function $S$`S`=$\frac{n\left(n+1\right)}{2}$`n`(`n`+1)2.

Easy

1min

In a room of $n$`n` people, if everyone shakes hands with everyone else, the total number of handshakes is given by $H=\frac{n\left(n-1\right)}{2}$`H`=`n`(`n`−1)2.

Easy

1min

An object is released $700$700 metres above ground and falls freely. The distance the object is from the ground is modelled by the formula $d=700-16t^2$`d`=700−16`t`2, where $d$`d` is the distance in metres that the object falls and $t$`t` is the time elapsed in seconds. This equation is graphed below.

Easy

1min

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