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Find a parabola with equation $ y = ax^2 + bx + c $ that has slope 4 at $ x = 1, $ slope -8 at $ x = -1, $ and passes through the point (2, 15).

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Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Hey, it's clear. So when you read here, so we apply is people to a X square plus B X plus c We take the derivative and it becomes to a X plus be the slope is for for access equal to one in the slope is a at Xs equal to negative one. We're just going to solve thes We're gonna add these up and yet be as equal to negative too. We could use the first or second equation to find a and we got A is equal to three. After we plug in for B, we note that the problem passes through two comma 15 so to find See, we just plug in 15 for a to square plus B times two plus c and we just put in the A and B values that we caught when we get four times three plus two times negative too plus C and we got see if people to seven. So the parabola is why is equal to three X square minus two x plus seven