 New Zealand
Level 8 - NCEA Level 3

Graphing Polynomial Functions

Interactive practice questions

Consider the function $f\left(x\right)=9x^2+18x-16$f(x)=9x2+18x16.

a

State the coordinates of the $y$y-intercept.

Give your answer in the form $\left(a,b\right)$(a,b).

b

Solve for the $x$x-value(s) of the $x$x-intercept(s).

If there is more than one value, write all of them on the same line, separated by commas.

c

Determine an equation for $f'\left(x\right)$f(x).

d

Hence solve for the $x$x-coordinate(s) of the stationary point(s).

If there is more than one, write all of them on the same line separated by commas.

e

By completing the table of values, find the gradient of the curve for the following values of $x$x:

$x$x $-2$2 $-1$1 $0$0
$f'\left(x\right)$f(x) $\editable{}$ $\editable{}$ $\editable{}$
f

Select the correct statement.

$\left(-1,-25\right)$(1,25) is a minimum turning point.

A

$\left(-1,-25\right)$(1,25) is a maximum turning point.

B

$\left(-1,-25\right)$(1,25) is a minimum turning point.

A

$\left(-1,-25\right)$(1,25) is a maximum turning point.

B
g

Draw the graph below.

Easy
Approx 8 minutes

Consider the function $f\left(x\right)=\left(3x-2\right)\left(x+3\right)$f(x)=(3x2)(x+3).

Consider the function $f\left(x\right)=\left(4x+5\right)^2\left(x-1\right)$f(x)=(4x+5)2(x1).

Consider the function $f\left(x\right)=\left(2x-1\right)^2\left(1-x\right)$f(x)=(2x1)2(1x).

Outcomes

M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

91578

Apply differentiation methods in solving problems