maths question

Watch this thread
daisychad98
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
Report Thread starter 4 months ago
#1
hello I was wondering if anyone could help me with this question
find the coordinates of the turning point on the curve with equation y=9+18x-3x^(2)
(4 marks)
thank you
gcse level higher non caculator
0
reply
mqb2766
Badges: 19
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Report 4 months ago
#2
(Original post by daisychad98)
hello I was wondering if anyone could help me with this question
find the coordinates of the turning point on the curve with equation y=9+18x-3x^(2)
(4 marks)
thank you
gcse level higher non caculator
have you tried completing the square?
1
reply
daisychad98
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3
Report Thread starter 4 months ago
#3
(Original post by mqb2766)
have you tried completing the square?
yes, i did
y = -3( x^2 - 6x - 3)
y = -3(( x-6)^2- 36-3)
y = -3(( x-6)^2- 39)
y = -3( x-6)^2- 117

than wasn't sure what to do next
0
reply
mqb2766
Badges: 19
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4
Report 4 months ago
#4
(Original post by daisychad98)
yes, i did
y = -3( x^2 - 6x - 3)
y = -3(( x-6)^2- 36-3)
y = -3(( x-6)^2- 39)
y = -3( x-6)^2- 117

than wasn't sure what to do next
The bold part isn't correct. Try expanding the x term in your answer you get 36x.

But when you complete the square, what do the terms represent in terms of a turning point.
0
reply
daisychad98
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#5
Report Thread starter 4 months ago
#5
(Original post by mqb2766)
The bold part isn't correct. Try expanding the x term in your answer you get 36x.

But when you complete the square, what do the terms represent in terms of a turning point.
y = -3( x^2 - 6x - 3)
y = -3(( x-3)^2- 9-3)
y = -3(( x-3)^2- 12)
y = -3( x-6)^2+36
ohh
so the coordinates are
(6,36)
i think the number inside the bracket is x and the number outside the bracket is y
and because x is inside the bracket you need to change the sign
thank you
0
reply
mqb2766
Badges: 19
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#6
Report 4 months ago
#6
(Original post by daisychad98)
y = -3( x^2 - 6x - 3)
y = -3(( x-3)^2- 9-3)
y = -3(( x-3)^2- 12)
y = -3( x-6)^2+36
ohh
so the coordinates are
(6,36)
i think the number inside the bracket is x and the number outside the bracket is y
and because x is inside the bracket you need to change the sign
thank you
Nearly there, see the bolds.
If you're unsure, just expand the completed square and check it matches the original quadratic.
0
reply
daisychad98
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#7
Report Thread starter 4 months ago
#7
(Original post by mqb2766)
Nearly there, see the bolds.
If you're unsure, just expand the completed square and check it matches the original quadratic.
oh yes, silly mistake
thank you
y = -3( x-3)^2+36
so it would be 3,36 ?
or do i have to times -3 by -3 first
0
reply
mqb2766
Badges: 19
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#8
Report 4 months ago
#8
(Original post by daisychad98)
oh yes, silly mistake
thank you
y = -3( x-3)^2+36
so it would be 3,36 ?
or do i have to times -3 by -3 first
Agree for the (x,y) point. A simple way to understand it is to sub x=3 into the expression.
What happens to the quadratic term? Why does this mean
y <= 36
in this case. What does the -3 multiplier affect?
Last edited by mqb2766; 4 months ago
0
reply
daisychad98
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#9
Report Thread starter 4 months ago
#9
(Original post by mqb2766)
Agree for the (x,y) point. A simple way to understand it is to sub x=3 into the expression.
What happens to the quadratic term? Why does this mean
y <= 36
in this case.
9+18x-3x^(2) = y
9+18x-3x^(2) = y
9+(18x3)-3^2x3=y
y=36
I'm not sure what happens to the quadratic term ?
thank you
Last edited by daisychad98; 4 months ago
0
reply
mqb2766
Badges: 19
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#10
Report 4 months ago
#10
y(3) = -3(3-3)^2 + 36 = -3*0 + 36 = 36
x=3 makes the quadratic term (x-3)^2 zero, so the quadratic is at a turning/stationary/extreme point. The value of the quadratic is simply the last term in the completed square expression. For x != 3, then
-3(x-3)^2 < 0
as the quadratic part is > 0 and multiplying it by -3 makes it < 0. So
y <= 36
The -3 multiplier affects the curvature of the quadratic, not the value of the turning point.
Last edited by mqb2766; 4 months ago
0
reply
daisychad98
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#11
Report Thread starter 4 months ago
#11
(Original post by mqb2766)
y(3) = -3(3-3)^2 + 36 = -3*0 + 36 = 36
x=3 makes the quadratic term (x-3)^2 zero, so the quadratic is at a turning/stationary/extreme point. The value of the quadratic is simply the last term in the completed square expression. For x != 3, then
-3(x-3)^2 < 0
as the quadratic part is > 0 and multiplying it by -3 makes it < 0. So
y <= 36
The -3 multiplier affects the curvature of the quadratic, not the value of the turning point.
oh that makes sense so it doesn't change the turning point
thank you for your help
1
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Were exams easier or harder than you expected?

Easier (3)
37.5%
As I expected (2)
25%
Harder (2)
25%
Something else (tell us in the thread) (1)
12.5%

Watched Threads

View All
Latest
My Feed