Question

The curve y = ax2 + bx + c touches the line y = x in the origin. It also touches the line y = 2x +3. Determine the function

Answer 1

by touhes theyy mean tangent to

Answer 2

i am getting a=-1/12, b=1, c=0, but let me check again

Answer 3

can u tell me how ?

Answer 4

well, the tangent touches the curve at origin.
so, the curve must go through origin, put x and y as 0, u will get c=0

Answer 5

yeah i got c=0 and b=1 but im stuck at a

Answer 6

put y=2x+3
then u will get a quadratic
make the discriminant 0
put c=0 and b=1 in that expression..
u will get a

Answer 7

got it? :)

Answer 8

nope :(

Answer 9

eh! why? u r facing problem in which point?

Answer 10

what is the discriminant ?

Answer 11

b^2-4ac

Answer 12

yeah i get 1+12a

Answer 13

when the quadratic is: ax^2+by+c=0

Answer 14

but why is 1+12a=0

Answer 15

u mean?

Answer 16

D=12a+1... u said i should make it equal to 0

Answer 17

means?

Answer 18

why should i make it =0 ??

Answer 19

as u have to make the discriminant 0 :)

Answer 20

why ?what is the rule ???

Answer 21

substitute y with with the expression of the tangent.. as the two roots will be same, discriminant will be 0. if u dont get it, go through quadratic chapter properly..

Answer 22

If b = 1 and c = 0 then you have y = ax^2+1x +0
But y = 2x+3 So: 2x+3 = ax^2 +x or ax^2 -x-3 = 0
But b^2-4ac must be 0 so (1)^2 - 4(a)(-3)=0
1+12a = 0 and a = -1/12

Answer 23

do we make it zero to only get one root ?

Answer 24

i envision something that looks like this

Answer 25

y = ax^2 + bx + c; (0,0), c=0

y = ax^2 + bx

y' = 2ax + b; (0,1), b=1
.....................................

y = ax^2 + x; y = 2x+3

ax^2 + x = 2x+3

ax^2 - x - 3 = 0

and since it can only touch in one spot, the determinate must equal 0

1-4(-3)(a)=0

1+12a=0

a = -1/12

i agree .....

Answer 26

ok now i got it ty all sry i was so annoying

Answer 27

'sok :)