hi all pls all

Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12

please solve the entire equation with explanation please. ty.

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- Feb 23rd 2008, 02:05 AMandrew2322tangent of a parabola
hi all pls all

Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12

please solve the entire equation with explanation please. ty. - Feb 23rd 2008, 04:29 AMPlato
- Feb 23rd 2008, 08:31 AMTheEmptySet

Since the line is written in slop intercept form

we know that the slope of line is

Since we need the slope to equal the derivative we get...

solving for x we get

This gives us half of the ordered pair...

plugging this into the equation of the parabola we get

This completes our ordered pair giving us (1,-12)

Now finally we use this ordered pair to solve for c plugging the ordered pair into the equation of the line we get....

solving for C we finally end up with...

I hope this helps. Remember that the derivative represents the slope of the graph at any point.(Rock)