Can anyone answer this GCSE cubic graph question?? (Draw suitable straight line to estimate sol'n to cubic)

Nirwanda

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Here is a question from Edexcel GCSE Maths mock exam Jan 2024:

On the grid draw the graph of y=x^3-3x+2

By drawing a suitable straight line on the grid, use your graph to find an estimate for the solution of

2x^3-3x+4=0

Give your answer correct to 1 decimal place



I rearranged equation 2 to give equation 1 on the left hand side, as follows:
x^3-3x+2=-x^3-2

I was expecting this to give a linear equation on the right hand side not a cubic

So plotting the graphs of y=x^3-3x+2 and y=-x^3-2 should give a solution to equation 2

And it does. These two graphs intersect at x=-1.6 which is roughly the solution to equation 2.

But y=-x^3-2 is not a straight line.

Any ideas what straight line they are after??

It’s GCSE so shouldn’t be too complex

Thanks
 
Here is the original question
 

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I rearranged equation 2 to give equation 1 on the left hand side, as follows:
x^3-3x+2=-x^3-2

I was expecting this to give a linear equation on the right hand side not a cubic
Yes, you are expected to get a linear function, so you need to do something that will cancel out the cubic term. Perhaps you need to divide the equation to be solved by 2 first?
 
Boy do I feel like an idiot :)

Yes of course that's it

So the straight line is y=-3x/2

Which gives intersect at x=-1.6

Thanks so much for your help Dr P

Spent ages looking at that. Couldn't see the wood for the trees
 
Yes indeed. For some reason I thought the 2x^3 term was written in stone and unchangeable
 
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