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maths question

f(x) = 2x^2 - x
g(x) = x^3

(iii) solve the equation f(x) = g(x)
I did 2x^2 - x = x^3
-x^3 + 2x^2 - x = 0
x = 1 and x = 0

but the answer says (0,0) so I'm confused
Reply 1
Avatar for Harribos
Harribos
7
Original post by Mia 15
f(x) = 2x^2 - x
g(x) = x^3

(iii) solve the equation f(x) = g(x)
I did 2x^2 - x = x^3
-x^3 + 2x^2 - x = 0
x = 1 and x = 0

but the answer says (0,0) so I'm confused

Those are for the coordinates

(0,0) and (1,1)

sub in x=0, 1 into one of the equations
(edited 3 years ago)
Reply 2
Avatar for davros
davros
16
Original post by Mia 15
f(x) = 2x^2 - x
g(x) = x^3

(iii) solve the equation f(x) = g(x)
I did 2x^2 - x = x^3
-x^3 + 2x^2 - x = 0
x = 1 and x = 0

but the answer says (0,0) so I'm confused

Can you upload a picture of the complete question? Are there other restrictions on x?
Reply 3
Avatar for Mia 15
Mia 15
OP
12
thanks I understand that part now but I was confused why the answer book just had (0,0) written for that question. because if the question says solve the equation f(x)=g(x) then shouldn't the answer just be the x values you found such as x=1 and x=0
Reply 4
Avatar for Mia 15
Mia 15
OP
12
Original post by davros
Can you upload a picture of the complete question? Are there other restrictions on x?


Sorry the picture won't upload but here's the question word for word:

Q) Two functions are given as f(x) = 2x^2 - x and g(x) = x^3.
(i) draw the graph
(ii) how many points of intersection are there? i wrote 2
(iii)
[a] solve the equation f(x) =g(x)
I did 2x^2 - x = x^3
-x^3 + 2x^2 - x = 0
x = 1 and x = 0

but the answer just says (0,0) so I'm confused

[b] hence find the coordinates of the points where the two curves intersect
when x=1, y = 2(1)^2 = 1 so (1,1)
when x=0, y=2(0)^2-0 so (0,0)

but the answer only says (1,1)


is this just an error in the answer book?
Reply 5
Avatar for mqb2766
mqb2766
21
Original post by Mia 15
Sorry the picture won't upload but here's the question word for word:

Q) Two functions are given as f(x) = 2x^2 - x and g(x) = x^3.
(i) draw the graph
(ii) how many points of intersection are there? i wrote 2
(iii)
[a] solve the equation f(x) =g(x)
I did 2x^2 - x = x^3
-x^3 + 2x^2 - x = 0
x = 1 and x = 0

but the answer just says (0,0) so I'm confused

hence find the coordinates of the points where the two curves intersect
when x=1, y = 2(1)^2 = 1 so (1,1)
when x=0, y=2(0)^2-0 so (0,0)

but the answer only says (1,1)


is this just an error in the answer book?

You realise the combined curve factorizes as
-x(x-1)^2
The curves graze at 1 (double root) but cross (intersect?) at 0
https://www.desmos.com/calculator/fckj5v9zbs
It would help to see the exact wording in the original question.
(edited 3 years ago)
Reply 6
Avatar for Mia 15
Mia 15
OP
12
Original post by mqb2766
You realise the combined curve factorizes as
-x(x-1)^2
The curves graze at 1 (double root) but cross (intersect?) at 0
https://www.desmos.com/calculator/fckj5v9zbs
It would help to see the exact wording in the original question.

Ohh I understand it now, thank you! :smile:

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