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Sketching Curves, C1 - please help :(

I was revising C1 and it seems I've forgotten what I did! :frown:

For example 1 on page 42.

The answer I got is (2,0) (1,0) (-1,0) with the curve crossing at (0,2).

My Maths teacher showed me a really easy way for finding whether the curve goes down or up. But, it seems I've forgotten it! :frown:

She showed me a method to find it out. It seemed multiplying some numbers and if the answer to those numbers is negative, the curve goes down. If positive, the curve goes up.

This is what she did for example to make it easy for me:

1 × 2 × 4 = 8 (number is positive so the graph goes up)

-4 × -3 × -1 = -12 (number is negative so it goes down)

I really can't figure out how she got these numbers but this was a really easy way for me to figure out iof the graph goes up or down.

Please help me! :frown:

Reply 1

jit987

What is the question?

Reply 2

Mo_H92

It is on page 42, example 1 of the main Edexcel C1 book.

The question just states this: Sketch the curve with the equation y = (x-2) (x-1) (x+1)

Reply 3

Mo_H92

Anyone?

This is driving me crazy!

Reply 4

EEngWillow

Original post by Mo_H92

Anyone?

This is driving me crazy!

In the form it's been given, you know the points where it crosses the x-axis. Mark these on your axes.

You can easily find where it crosses the y-axis by multiplying the three constants together. Mark this on your axes.

That's basically all you need - the rest is joining dots.

Reply 5

Mo_H92

I got where it crosses the Y-Axis. I just don't know if the curve should go up or down or if which side it should be :frown:

Reply 6

ixion10

Original post by Mo_H92

It is on page 42, example 1 of the main Edexcel C1 book.

The question just states this: Sketch the curve with the equation y = (x-2) (x-1) (x+1)

At x axis, y=0, therefore: 0=(x-2) (x-1) (x+1), so x=2, 1, -1

At y axis, x=0, so y=(0-2) (0-1) (0+1)= -2*-1*1= 2

Therefore the graph crosses the x axis at points: (2,0) (1,0) and (-1,0)
and y axis at (0,2)

Sketch this and thats your answer.

You are welcome in advance :biggrin:

Reply 7

v2p

Original post by Mo_H92

I got where it crosses the Y-Axis. I just don't know if the curve should go up or down or if which side it should be :frown:

If you've plotted the 4 points like in the first diagram shown, there should really be only one way you can draw the S shape of a cubic graph. Try trying to draw the graph another way just looking at those 4 points, you should find it just doesn't work out.

Heres my attempt at trying to show you what I mean.
http://img848.imageshack.us/i/c1image.jpg/

------------------------------------------

But anyway, that aside, the simplest way is to look at the equation in

x^3

form.
This may require expanding it to

x^3-2 x^2-x+2

It's a bit difficult to describe but hopefully you understand this:
If

x^3

is positive, this means the shape of the curve goes (from left to right) up, then down, then up.
So basically if x^3 is positive, (from left to right) start underneath the x axis, then go up and cross the x axis on your left-most point on the x-axis, then loop off this curve and come back down crossing the x-axis on your middle point, then loop off this curve, and come back up through the right-most point on the x-axis.