R146
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The curve y=p^x +2qx passes through the points (1,4) and (-1,-3/2)
Given that y<0 at x=-5 find the values of p and q
Any help would be greatly appreciated!
Thank you for reading
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mqb2766
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(Original post by R146)
The curve y=p^x +2qx passes through the points (1,4) and (-1,-3/2)
Given that y<0 at x=-5 find the values of p and q
Any help would be greatly appreciated!
Thank you for reading
Sub the points and solve the simultaneous equations.
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R146
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(Original post by mqb2766)
Sub the points and solve the simultaneous equations.
Thank you!Sorry to disturb but by that do you mean (1,4) and (-1,-3/2)? or y is 0 and x is -5
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mqb2766
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(Original post by R146)
Thank you!Sorry to disturb but by that do you mean (1,4) and (-1,-3/2)? or y < 0 and x is -5
The bold is not a point.
See what you get by subbing/solving the two points and think about why they've given you the extra constraint.
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R146
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(Original post by mqb2766)
The bold is not a point.
See what you get by subbing/solving the two points and think about why they've given you the extra constraint.
Thank you once again i am beginning to understand this!
I have gotten:
1=p^4+8q (1)
-3/2=p^-1-2q (2)
i Then did equation (2)x4 so it became:
-6=4p-8q
I have got -5=4p+p^4
I hope that is correct so far!
Thank you for your time again
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mqb2766
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(Original post by R146)
Thank you once again i am beginning to understand this!
I have gotten:
1=p^4+8q (1)
-3/2=p^-1-2q (2)
i Then did equation (2)x4 so it became:
-6=4p-8q
I have got -5=4p+p^4
I hope that is correct so far!
Thank you for your time again
You don't normally solve quartics at a level. Check the x-y values youve subbed. Also make sure you know what p^(-1) represents.
Last edited by mqb2766; 3 weeks ago
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R146
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(Original post by mqb2766)
You don't normally solve quartics at a level. Check the x-y values youve subbed. Also make sure you know what p^(-1) represents.
Sorry ive only recently started a levels so i may be a bit of a newbie,thank you for putting up with me
This might be wrong but i redid the equation and i got
4=p+2q
-3/2=1/p-2q
5/2=1/p+p?
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mqb2766
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(Original post by R146)
Sorry ive only recently started a levels so i may be a bit of a newbie,thank you for putting up with me
This might be wrong but i redid the equation and i got
4=p+2q
-3/2=1/p-2q
5/2=1/p+p?
Yes, so solve for p. If you multiply through by p it becomes a quadratic which is bread and butter ...
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STARFIRE13245
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(Original post by R146)
The curve y=p^x +2qx passes through the points (1,4) and (-1,-3/2)
Given that y<0 at x=-5 find the values of p and q
Any help would be greatly appreciated!
Thank you for reading
Given,

y=px
2
+qx+r

at (0,0) we get,

0=p(0)
2
+q(0)+r

∴r=0

dx
dy

=2px+q →y=x,m=1

dx
dy

(0,0)

=2p(0)+q=1

⇒q=1

y=px
2
+q at (1,2)

2=p(1)
2
+1

⇒p=1

∴p=1,q=1,r=0
hope that i helped you
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mqb2766
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(Original post by STARFIRE13245)
Given,

....
Can you pls delete and read the sticky at the top of the forum about posting hints, not "solutions".
Last edited by mqb2766; 3 weeks ago
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R146
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(Original post by mqb2766)
Yes, so solve for p. If you multiply through by p it becomes a quadratic which is bread and butter ...
Thank you once again!I have gotten
(2p−1)(p−2)=0
Giving p=1/2 or 2
I assume you just sub that back in to find q as you usually do?
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mqb2766
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(Original post by R146)
Thank you once again!I have gotten
(2p−1)(p−2)=0
Giving p=1/2 or 2
I assume you just sub that back in to find q as you usually do?
Sure. Then use the final constraint.
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(Original post by mqb2766)
Can you pls delete and read the sticky at the top of the forum about posting hints, not "solutions".
sorry i did not understand
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R146
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(Original post by mqb2766)
Sure. Then use the final constraint.
I got q is 1.75 if p is 0.5 and q is 1 if p is 2
Im not sure where y<0 so x=-5 comes in though
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mqb2766
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(Original post by R146)
I got q is 1.75 if p is 0.5 and q is 1 if p is 2
Im not sure where y<0 so x=-5 comes in though
What happens to those solutions when x=-5?
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Muttley79
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(Original post by STARFIRE13245)
sorry i did not understand
Delete post #9 - you have btoken the forum rules
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ok sorry i did not know
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R146
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(Original post by mqb2766)
What happens to those solutions when x=-5?
Thank you so so much for this once again,this has been great learning and really helpful,i figured out that only one of them were correct and that was p=1 and q=2!
Thank you so much again and i wish you well in the future
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