# Confusion over function/graph question A Level

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I don't understand how to finish off this question.

I've worked out the equation of the line being y = 6x + 25, but I'm not quite sure what to do next. I imagine the next step is finding the equation of the parabola. Would this just be (x+2)^2 + 13, or do I have to assume an unknown coefficient?

I've worked out the equation of the line being y = 6x + 25, but I'm not quite sure what to do next. I imagine the next step is finding the equation of the parabola. Would this just be (x+2)^2 + 13, or do I have to assume an unknown coefficient?

Last edited by frogstuga; 1 month ago

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#3

Given the turning point, you get y = (x+2)^2 + 13, but the intercept of this graph would be 17, so you would have to scale the (x+2)^2 term by a coefficient such that the intercept becomes 25.

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#4

It should y = a(x+2)^2 + 13 and then get the value of a from the y-intercept of graph.

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(Original post by

It should y = a(x+2)^2 + 13 and then get the value of a from the y-intercept of graph.

**deskochan**)It should y = a(x+2)^2 + 13 and then get the value of a from the y-intercept of graph.

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#6

(Original post by

Ahhhhhhh that makes sense now and I see the connection. For the inequality, am I supposed to show that the area is above the quadratic between the points and below the straight line?

**frogstuga**)Ahhhhhhh that makes sense now and I see the connection. For the inequality, am I supposed to show that the area is above the quadratic between the points and below the straight line?

Last edited by mqb2766; 1 month ago

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(Original post by

Yes. It needs to satisfy both inequalities. There is no need to mention the points, obviously.

**mqb2766**)Yes. It needs to satisfy both inequalities. There is no need to mention the points, obviously.

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#8

(Original post by

How would I go about doing it? I've never seen a question asking something like this so I'm thoroughly confused even though I'll probably kick myself.

**frogstuga**)How would I go about doing it? I've never seen a question asking something like this so I'm thoroughly confused even though I'll probably kick myself.

* above the quadratic

* below the lilne

R is then the intersection of the two. This talks about lilnear inequalities.

https://www.youtube.com/watch?v=rq4N...l=MathswithJay

There are probably better videos/pdfs (textbook?) to describe an inequality.

Last edited by mqb2766; 1 month ago

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#9

If i have understood the question correctly. It is looking for the area of R.

I would do this by integration to find the area below the curve C between the points x=0 and x = -2.

To find this line you would use y = a(x - b)

In your case it would be:

y = a(x+2)

y = a(x

Using the y intercept to solve for a

25 = a(0 + 0 + 4) + 13

12 = 4a

a = 3

Therefore the curve is y = 3x

Explained well here

https://www.google.com/search?client...V1fAPpquk8Ac25

I would then work out the area of what is below the line L for the same points. This can be done with either integration or just area of a triangle.

Then subtract the area below the curve from the area below the line. This should give you R

Sorry, I am not going to go through the integration.

Hope that helps.

I would do this by integration to find the area below the curve C between the points x=0 and x = -2.

To find this line you would use y = a(x - b)

^{2}+ c where (b,c) is the turning point.In your case it would be:

y = a(x+2)

^{2}+13y = a(x

^{2}+4x + 4) + 13Using the y intercept to solve for a

25 = a(0 + 0 + 4) + 13

12 = 4a

a = 3

Therefore the curve is y = 3x

^{2}+12x +25Explained well here

https://www.google.com/search?client...V1fAPpquk8Ac25

I would then work out the area of what is below the line L for the same points. This can be done with either integration or just area of a triangle.

Then subtract the area below the curve from the area below the line. This should give you R

Sorry, I am not going to go through the integration.

Hope that helps.

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#10

This question is really interesting because it needs us to express the answers in a set of inequalities.

This makes me recall the linear programming and graph an area where inequalities overlap. So, what should we do?

we should write all the constraints to enclose the area R.

e.g. y = 6x +25; think about the put (0,0) into it and we can see 0 = 25, ie. 0<25. Yeah, we approach it as y<= 6x +25

then how about parabola? how about x-axis and y axis boundries?

This makes me recall the linear programming and graph an area where inequalities overlap. So, what should we do?

we should write all the constraints to enclose the area R.

e.g. y = 6x +25; think about the put (0,0) into it and we can see 0 = 25, ie. 0<25. Yeah, we approach it as y<= 6x +25

then how about parabola? how about x-axis and y axis boundries?

Last edited by deskochan; 1 month ago

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#11

(Original post by

If i have understood the question correctly. It is looking for the area of R.

....

**mark1666**)If i have understood the question correctly. It is looking for the area of R.

....

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(Original post by

If i have understood the question correctly. It is looking for the area of R.

I would do this by integration to find the area below the curve C between the points x=0 and x = -2.

To find this line you would use y = a(x - b)

In your case it would be:

y = a(x+2)

y = a(x

Using the y intercept to solve for a

25 = a(0 + 0 + 4) + 13

12 = 4a

a = 3

Therefore the curve is y = 3x

Explained well here

https://www.google.com/search?client...V1fAPpquk8Ac25

I would then work out the area of what is below the line L for the same points. This can be done with either integration or just area of a triangle.

Then subtract the area below the curve from the area below the line. This should give you R

Sorry, I am not going to go through the integration.

Hope that helps.

**mark1666**)If i have understood the question correctly. It is looking for the area of R.

I would do this by integration to find the area below the curve C between the points x=0 and x = -2.

To find this line you would use y = a(x - b)

^{2}+ c where (b,c) is the turning point.In your case it would be:

y = a(x+2)

^{2}+13y = a(x

^{2}+4x + 4) + 13Using the y intercept to solve for a

25 = a(0 + 0 + 4) + 13

12 = 4a

a = 3

Therefore the curve is y = 3x

^{2}+12x +25Explained well here

https://www.google.com/search?client...V1fAPpquk8Ac25

I would then work out the area of what is below the line L for the same points. This can be done with either integration or just area of a triangle.

Then subtract the area below the curve from the area below the line. This should give you R

Sorry, I am not going to go through the integration.

Hope that helps.

That's a great help though thank you very much.

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(Original post by

This question is really interesting because it needs us to express the answers in a set of inequalities.

This makes me recall the linear programming and graph an area where inequalities overlap. So, what should we do?

we should write all the constraints to enclose the area R.

e.g. y = 6x +25; think about the put (0,0) into it and we can see 0 = 25, ie. 0<25. Yeah, we approach it as y<= 6x +25

then how about parabola? how about x-axis and y axis boundries?

**deskochan**)This question is really interesting because it needs us to express the answers in a set of inequalities.

This makes me recall the linear programming and graph an area where inequalities overlap. So, what should we do?

we should write all the constraints to enclose the area R.

e.g. y = 6x +25; think about the put (0,0) into it and we can see 0 = 25, ie. 0<25. Yeah, we approach it as y<= 6x +25

then how about parabola? how about x-axis and y axis boundries?

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#14

(Original post by

That's the issue I'm having. I'm sure the actual inequality is relatively simple and will make me kick myself, but I've just never seen a question asking me to show it in terms of inequalities.

**frogstuga**)That's the issue I'm having. I'm sure the actual inequality is relatively simple and will make me kick myself, but I've just never seen a question asking me to show it in terms of inequalities.

https://www.bbc.co.uk/bitesize/guide...qhv/revision/4

I can't see that much a level content in this question

Last edited by mqb2766; 1 month ago

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(Original post by

Where does the question come from? Describing inequalities is covered at gcse

https://www.bbc.co.uk/bitesize/guide...qhv/revision/4

I can't see that much a level content in this question

**mqb2766**)Where does the question come from? Describing inequalities is covered at gcse

https://www.bbc.co.uk/bitesize/guide...qhv/revision/4

I can't see that much a level content in this question

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#16

(Original post by

This is from the Edexcel A Level 2021 Assessment Materials. This is definitely A Level content as we covered regions like these in Year 12.

**frogstuga**)This is from the Edexcel A Level 2021 Assessment Materials. This is definitely A Level content as we covered regions like these in Year 12.

https://www.youtube.com/watch?v=aexv...l=corbettmaths

https://www.youtube.com/watch?v=8J_m...l=corbettmaths

Last edited by mqb2766; 1 month ago

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(Original post by

Just saying the material necessary to answer the question is largely covered at gcse (completing the square, equation of a line, graph inequalities). There is a bit more "higher" content in terms of estimating the quadratic parameters from the points, but not a lot. So yes, A level, but not by much. You could get inequality region description questions at gcse, or when a quadratic curve is less than a line (quadratic iniequalities - gcse), or as the other poster notes, its a fundamental in linear programming (A level option), ... so it shouldn't be too surprising.

https://www.youtube.com/watch?v=aexv...l=corbettmaths

https://www.youtube.com/watch?v=8J_m...l=corbettmaths

**mqb2766**)Just saying the material necessary to answer the question is largely covered at gcse (completing the square, equation of a line, graph inequalities). There is a bit more "higher" content in terms of estimating the quadratic parameters from the points, but not a lot. So yes, A level, but not by much. You could get inequality region description questions at gcse, or when a quadratic curve is less than a line (quadratic iniequalities - gcse), or as the other poster notes, its a fundamental in linear programming (A level option), ... so it shouldn't be too surprising.

https://www.youtube.com/watch?v=aexv...l=corbettmaths

https://www.youtube.com/watch?v=8J_m...l=corbettmaths

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