Graph Cubic Curves

Topics

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 2

1. Question
Sketch the graph of the cubic curve for the equation below

$y=2(x+1)(x-4)(x-6)$
- 1.
- 2.
- 3.
- 4.
Hint

Help Video
Correct

Nice Job!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

The standard form for graphing a cubic is $y=a(x-r)(x-s)(x-t)$ .

The sign of $a$ in this equation tells us the shape of the graph

In this equation $a=2$ which is positive.

Therefore this is a positive cubic curve and has the approximate shape shown below:

Find the $x$ -intercepts of the graph by setting $y=0$ .

$2$ $(x+1)$ $(x-4)$ $(x-6)$ $=0$

So $x+1=0$ , $x-4=0$ or $x-6=0$

This means $x=-1$ , $x=4$ or $x=6$ .

This gives us $x$ -intercepts $-1$ , $4$ and $6$ which we mark on the $x$ -axis

Find the $y$ -intercepts of the graph by setting $x=0$ .

$y=2(0+1)(0-4)(0-6)$

$y=2\cdot (1) \cdot (-4)\cdot (-6)$

$y=48$

This gives us a $y$ -intercept of $48$ which we mark on the $y$ -axis

Draw a positive cubic curve which passes through the intercepts found.
Question 2 of 2

2. Question
Sketch the graph of the cubic curve for the equation below

$y=-2(x-1)(x+2)(x+4)$
- 1.
- 2.
- 3.
- 4.
Hint

Help Video
Correct

Well Done!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

The standard form for graphing a cubic is $y=a(x-r)(x-s)(x-t)$ .

The sign of $a$ in this equation tells us the shape of the graph

In this equation $a=-2$ which is negative.

Therefore this is a negative cubic curve and has the approximate shape shown below:

Find the $x$ -intercepts of the graph by setting $y=0$ .

$-2$ $(x-1)$ $(x+2)$ $(x+4)$ $=0$

So $x-1=0$ , $x+2=0$ or $x+4=0$

This means $x=1$ , $x=-2$ or $x=-4$ .

This gives us $x$ -intercepts $1$ , $-2$ and $-4$ which we mark on the $x$ -axis

Find the $y$ -intercepts of the graph by setting $x=0$ .

$y=-2(0-1)(0+2)(0+4)$

$y=-2\cdot (-1) \cdot (2)\cdot (4)$

$y=16$

This gives us a $y$ -intercept of $16$ which we mark on the $y$ -axis

Draw a negative cubic curve which passes through the intercepts found.

Graph Cubic Curves

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Nice Job!

2. Question

Hint

Well Done!

Quizzes