Find all tangent lines to y = x^2 + 2x + 1 that pass through (0, -15)

Question

anonymous · Answer

First find the derivative of that function

anonymous · Answer

Yeah, it's 2x + 2

anonymous · Answer

then plug in the x-coordinate value given by your point (this will be your slope of the derivative "tangent" line)

anonymous · Answer

The slope is 2

anonymous · Answer

Correct.  Now using that, you can plug the coordinate and your new slope in the point slope formula 

$$y-y _{1}=m \left( x-x _{1} \right)$$

anonymous · Answer

y+ 15 = 2x

anonymous · Answer

If you get y to one side, then you'll notice that it looks like slope/intercept formula and that will be your tangent line

anonymous · Answer

Is that all the tangent lines?

anonymous · Answer

To my knowledge there can be multiple tangent lines to a function but only one per point (and you're only given one coordinate)

freckles · Answer

It doesn't say find the tangent line at (0,-15)

anonymous · Answer

Okay. It's just that I gave basically the same answer on my test for this question and got it wrong.

anonymous · Answer

It says it passes through, I thought it was the same thing

freckles · Answer

solve the following equation for a first:
$$\frac{dy}{dx}|_{(x,y)=(a,f(a))}=\frac{f(a)-(-15)}{a-0}$$

freckles · Answer

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