# Math Help - tangent of a parabola

1. ## tangent 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

2. Originally Posted by andrew2322
Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12
The slope at each point on the parabola is 2x-1.
Now why don't you show us what you have done on your own.

3. $\frac{dy}{dx}=2x-1$

Since the line is written in slop intercept form
$y=x+c$ we know that the slope of line is
$m=1$

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

$1=2x-1$ solving for x we get

$x=1$ This gives us half of the ordered pair...

plugging this into the equation of the parabola we get

$y=(1)^2-(1)-12=-12$ 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....
$-12=1+C$ solving for C we finally end up with...

$y=x-13$

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