# Sketching Graphs - Misconception

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#1
Hi guys, in the graph y = 4x^3 - 24x^2 ,

How am I meant to sketch this graph ? I know the general shape of a cubic graph, I know the roots are 0 and 6.

But how am I meant to know whether the part of the curve between x = 0 and x = 6 is above or below the x - axis ?

I lost about 4 marks because of this lack of knowledge in my exam.

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1 month ago
#2
(Original post by lhh2003)
Hi guys, in the graph y = 4x^3 - 24x^2 ,

How am I meant to sketch this graph ? I know the general shape of a cubic graph, I know the roots are 0 and 6.

But how am I meant to know whether the part of the curve between x = 0 and x = 6 is above or below the x - axis ?

I lost about 4 marks because of this lack of knowledge in my exam.

Easy. The graph is continuous and you know that for large negative values it will be negative, and for large positive values it will be positive. How can you make this work with those two roots?

More importantly, get yourself a graphics calculator. It would have saved you those marks, and maybe others. People who tell you they are of no use probably don't know how to use them well: which includes most teachers.
1
1 month ago
#3
(Original post by lhh2003)
Hi guys, in the graph y = 4x^3 - 24x^2 ,

How am I meant to sketch this graph ? I know the general shape of a cubic graph, I know the roots are 0 and 6.

But how am I meant to know whether the part of the curve between x = 0 and x = 6 is above or below the x - axis ?

I lost about 4 marks because of this lack of knowledge in my exam.

Plug a value (which is between 0 and 6) into the equation.

If your result is positive, then y is positive hence the curve is above the x axis.

Similarly if the result is negative.
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1 month ago
#4
"I know the roots are 0 and 6" isn't strictly true. The roots are 0, 0 and 6. What does the repeated root mean graphically?
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1 month ago
#5
(Original post by lhh2003)
Hi guys, in the graph y = 4x^3 - 24x^2 ,

How am I meant to sketch this graph ? I know the general shape of a cubic graph, I know the roots are 0 and 6.

But how am I meant to know whether the part of the curve between x = 0 and x = 6 is above or below the x - axis ?

I lost about 4 marks because of this lack of knowledge in my exam.

All of the above and also factorise
4x^2(x-6)
The graph is negative (not positive) for x<6.
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#6
(Original post by David Getling)
Easy. The graph is continuous and you know that for large negative values it will be negative, and for large positive values it will be positive. How can you make this work with those two roots?

More importantly, get yourself a graphics calculator. It would have saved you those marks, and maybe others. People who tell you they are of no use probably don't know how to use them well: which includes most teachers.
They are like £100
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#7
(Original post by RDKGames)
Plug a value (which is between 0 and 6) into the equation.

If your result is positive, then y is positive hence the curve is above the x axis.

Similarly if the result is negative.
Thank you.
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#8
(Original post by dextrous63)
"I know the roots are 0 and 6" isn't strictly true. The roots are 0, 0 and 6. What does the repeated root mean graphically?
Very true. I guess it means that the graph will have to go under the x axis from point 0 until it reaches point 6
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1 month ago
#9
(Original post by lhh2003)
Very true. I guess it means that the graph will have to go under the x axis from point 0 until it reaches point 6
Correct
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1 month ago
#10
(Original post by dextrous63)
"I know the roots are 0 and 6" isn't strictly true. The roots are 0, 0 and 6. What does the repeated root mean graphically?
A repeated root often means that you have a maximum or minimum touching the x axis.
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1 month ago
#11
(Original post by lhh2003)
They are like £100
Well think of it like this. Over the two years you spend taking your A-levels that works out to £1 a week. Isn't spending that each week worth it if it gets you a higher grade? Think of how much money most students waste on their mobile phones.
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1 month ago
#12
(Original post by David Getling)
Well think of it like this. Over the two years you spend taking your A-levels that works out to £1 a week. Isn't spending that each week worth it if it gets you a higher grade? Think of how much money most students waste on their mobile phones.
Plus, of course, at the end of it all there are internet auction sites available to recoup a substantial amount of the investment if needs be.
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1 month ago
#13
(Original post by dextrous63)
Plus, of course, at the end of it all there are internet auction sites available to recoup a substantial amount of the investment if needs be.
Bang on! One of my students bought a second-hand TI-Nspire CX.
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1 month ago
#14
(Original post by David Getling)
Bang on! One of my students bought a second-hand TI-Nspire CX.
Whether one opts for Texas or Casio, there are also a couple of highly rated books available to explain how to use them
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