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Find the parabola with equation $ y = ax^2 + bx $ whose tangent line at (1, 1) has equation $ y = 3x - 2. $

$$y=2 x^{2}-x$$

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Missouri State University

Harvey Mudd College

Baylor University

Idaho State University

he It's clear someone You right here. So we have a problem. Why is equal to a X square plus B X and the point one comma one? So we get one is equal to a plus B The slope of the tension at one comma one is the derivative of our problem. That X is equal to one. Do you? I over D X is equal to two x plus b and we plug in X is equal to one to get to a plus B on our equation is why is equal to three X minus two and the slope is three. So the equation of the 10 general one comma one is three So he can write this as to a plus, B is equal to three. We're gonna subtract a plus B is equal to one. Then we get a is equal to two. We just substitute a to find B and we got B is equal to negative one. So the equation of our problem is why is equal to two x square minus assets