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Draw a diagram to shoe that there are two tangent lines to the parabola $y = x^2$ that pass through the point (0, -4). Find the coordinates of the point where these tangent lines intersect the parabola.

$\left(a, a^{2}\right)$ also lies on the line, $a^{2}=2 a(a)-4,$ or $a^{2}=4 .$ So $a=\pm 2$ and the points are (2,4)and (-2,4)

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Anna Marie V.

Campbell University

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Oregon State University

Samuel H.

University of Nottingham

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Hey, it's Claire. So when you read here So we're gonna note that all points of the problem Why equals X square or the form ex calmer X square in the 10 gin A comma a square pass History zero common negative floor We know that the slope of attention at any point is the derivative. So when we do a friend a tree we have two x So the slough off the tension at a comma A square iss to a And since this tension passes street of slope Hey, do the 0.8 common Any square and zero common negative four. We can write the slip detention as a square plus four over a which is equal to to a and then we get a is equal to positive or negative too. One of the tensions is to come before and the other is negative to Palmer for when we draw a graph, it looks like this men are tensions are gonna be in blue. This is Siro common negative for to karma four negative too common for

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Samuel H.

University of Nottingham

Lectures

Join Bootcamp