New Zealand
Level 7 - NCEA Level 2

# Solve applications involving cubic functions

## Interactive practice questions

Consider the function $f\left(x\right)=x^3-7x^2+4x+12$f(x)=x37x2+4x+12.

a

Is $6$6 a zero of the function?

Yes

A

No

B

Yes

A

No

B
b

Is $-1$1 a zero of the function?

Yes

A

No

B

Yes

A

No

B
c

Is $3$3 a zero of the function?

Yes

A

No

B

Yes

A

No

B
Easy
Approx a minute

Consider the function $f\left(x\right)=x^4-7x^3+12x^2+4x-16$f(x)=x47x3+12x2+4x16.

The mass in kilograms of a cubic container of water is given by $M=0.001r^3$M=0.001r3 where $r$r is the side length of the cube shaped container in centimetres.

The volume of a sphere has the formula $V=\frac{4}{3}\pi r^3$V=43πr3. The graph relating $r$r and $V$V is shown.

### 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