New Zealand
Level 7 - NCEA Level 2

# Interpret key features of quadratic graphs

## Interactive practice questions

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=16t2, 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.

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

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
Less than a minute

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.

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(n1)2.

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=70016t2, 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.

### Outcomes

#### M7-2

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

#### 91257

Apply graphical methods in solving problems