Math help (urgent)

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

Reply 1

mqb2766

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.

Reply 2

R146

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

Reply 3

mqb2766

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.

Reply 4

R146

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

Reply 5

mqb2766

Original post by R146

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.

(edited 2 years ago)

Reply 6

R146

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?

Reply 7

mqb2766

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 ...

Reply 8

STARFIRE13245

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

Reply 9

mqb2766

Original post by STARFIRE13245

Given,

....

Can you pls delete and read the sticky at the top of the forum about posting hints, not "solutions".

(edited 2 years ago)

Reply 10

R146

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?

Reply 11

mqb2766

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.

Reply 12

STARFIRE13245

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

Reply 13

R146

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

Reply 14

mqb2766

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?

Reply 15

Muttley79

Original post by STARFIRE13245

sorry i did not understand

Delete post #9 - you have btoken the forum rules

Reply 16

STARFIRE13245

ok sorry i did not know

Reply 17

R146

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