Question

the curve y=ax2+bx+c passes through the point(1,2) and is tangent to the line y=x at the origin.find a,b and c..........in ax2......2 is a power of x

Answer 1

Eh, here's something you can do.
You can put in the given information like this:
(2)=a(1)^2+b(1)+c
(0)=a(0)^2+b(0)+c
Then find a, b, and c such that ax^2+bx+c=x has only one solution (can use discriminant test or something like that).

Answer 2

no...we have to solve it by taking derivative rule and slope.........but how????

Answer 3

Derivative of quadratic gives slope of tangent line

Answer 4

Oh, if you know calculus, that'll be a lot easier.

Answer 5

and the y intercept for the quadratic is pretty clear

Answer 6

what @estudier is telling you is if the line \(y=x\) is tangent at the origin, then the value of function at the origin must be the same a \(y=x\) at the origin, namely \(0\) so you know \(c=0\)

Answer 7

Take derivative of ax^2+bx. You know c has to =0, so just leave it out.

Answer 8

could any solve it and tell me the answer of a and b????

Answer 9

You can do it.
What is the first derivative of ax^2+bx?

Answer 10

2ax+b

Answer 11

Derivative equals slope of the tangent line, so set that equal to the slope of the tangent line.

Answer 12

we would use the value of x in 2ax that is one....right????

Answer 13

The value of x at the point of tangency is 0. The slope of the tangent line is 1.

Answer 14

no...i am talking about the curve that passes through the point (1,2)

Answer 15

Yes, me too.

Answer 16

"...and is tangent to the line y=x at the origin."
The line is tangent at x=0.

Answer 17

so i think b=-1...

Answer 18

Derivative = slope
Derivative = 2ax+b
Slope = 1
2ax+b=1
x=0 at point of tangency.
2a(0)+b=1

Yes?

Answer 19

yeah....but what about a????

Answer 20

Now you can use the point (1,2) to find that.

Answer 21

oh yes.....its done a=1.....thankyou.....

Answer 22

You're welcome.