Show that the tangent to P: y= ax^2+bx+c with gradient m has y intercept c-(m-b)^2/4a. thank you.

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- April 25th 2009, 07:37 PMslaypullingcatderivative application
Show that the tangent to P: y= ax^2+bx+c with gradient m has y intercept c-(m-b)^2/4a. thank you.

- April 25th 2009, 07:44 PMThe Second Solution
- April 25th 2009, 08:07 PMSoroban
Hello, slaypullingcat!

The procedure is simple, but there's a LOT of algebra!

I was lucky to get the answer on the first try . . .

Quote:

Show that the tangent to: . with gradient

. . has y-intercept: .

The derivative of: . [1] .is: .

If the gradient is

Substitute into [1]: .

The tangent has point . and slope

Its equation is: .

. .

- April 25th 2009, 08:31 PMslaypullingcat
That was a quality post, thank you very much. I understand it now.