Functions (Graphs and Behaviour)

Hong Kong

Stage 4 - Stage 5

Consider the quadratic function $f\left(x\right)=x^2-2x-8$`f`(`x`)=`x`2−2`x`−8.

a

Complete the following table of values.

$x$x |
$-9$−9 | $-3$−3 | $0$0 | $5$5 | $9$9 |

$f\left(x\right)$f(x) |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

Hence sketch the curve.

Loading Graph...

c

Choose all the correct statements.

The curve is steeper at $x=6$`x`=6 than at $x=1$`x`=1.

A

The curve is parabolic in shape and is concave up.

B

At the point $f\left(n\right)$`f`(`n`), the function takes the value of $n$`n`.

C

The curve has $x$`x`-intercepts at $-2$−2 and $4$4.

D

At the point $n$`n`, the function takes the value of $f\left(n\right)$`f`(`n`).

E

As the value of $a$`a` is positive, the curve is concave down.

F

Easy

Approx 5 minutes

Consider the quadratic function $f\left(x\right)=-3\left(x-3\right)\left(x+1\right)$`f`(`x`)=−3(`x`−3)(`x`+1).

Consider the cubic function $f\left(x\right)=2x^3+4x^2$`f`(`x`)=2`x`3+4`x`2.

Consider the cubic function $f\left(x\right)=2x^3-2$`f`(`x`)=2`x`3−2.

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