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How to find the point a tangent line hits when given a point off of the graph. 
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#1
Feb512, 02:39 PM

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1. The problem statement, all variables and given/known data
(a) Draw a diagram to show that there are two tangent lines to the parabola y = x^2 that pass through the point (0, 4). (Do this on paper. Your teacher may ask you to turn in this work.) (b) Find the coordinates of the points where these tangent lines intersect the parabola. ( , ) (point with smaller x value) ( , ) (point with larger x value) 3. The attempt at a solution I drew the graph of y=x^2, I also drew the point (0,4) and I drew estimated tangent lines. I just don't understand how I go about finding the point where both of these tangent lines hit, I can estimate it but I know it's not looking for that. I first got the derivative at 0 but realized that that is not the way to go about answering this. 


#2
Feb512, 02:45 PM

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Take (x,x^2) to be a point on your parabola. What's the slope of the tangent line there using the derivative? Now the line through (x,x^2) and (0,4) has to have that same slope. How would you express that condition?



#3
Feb512, 02:52 PM

P: 9

Okay, so the slope would be 2x at (x,x^2) correct? I don't really understand that point though and where it exists on the graph, also how it has the same slope as that of (0,4).
So, now that I know the slope I can figure out where the line hits the graph right? I just don't really know how to do that either honestly. 


#4
Feb512, 03:16 PM

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How to find the point a tangent line hits when given a point off of the graph.



#5
Feb512, 09:05 PM

P: 9

This helped a lot! I got the answer.



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