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Sketch the parabolas $ y = x^2 and $ y = x^2 - 2x + 2. $ Do you think there is a line that is tangent to both curves? If so. find its equation. If not, why not?

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Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

he is Claire's. So when you're in here, so we're gonna sketch are two parabolas. I'm gonna sketch our first. Why is equal to X square with black and the other one in red? There are two problems. Look us follows and ver y is equal to x square. You get the derivative to be two x confer. Why is equal to X square nine is two X plus two we get to X minus two. So we're gonna use the equation. Why is equal to X plus be? And that's tension to why is equal two X square at X sub one comma ex subway in square and for why is equal to X square minus two X plus two We get X sub too on the except to square minus two except two plus two. So we get the equation. A is equal to a to accept one which is equal to to accept to minus two Your ex Someone square is equal to a X sub one It must be we get except to square minus two except two plus two is equal to a except two plus B And from our equation we get except one is equal to a over to on except to is equal to a over to plus one. And when we put it into our equations, we gotta be value of negative. 1/4 a square and B is equal to needed of 1/4 a square minus a plus one. We're a second equation. So when we set these equal to each other older right here, negative 1/4 a square is equal to negative 1/4 a square minus a plus one. We get a is equal to one B is equal to negative 1/4. So the equation we get is why is equal to X minus 1/4?