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[math SL] Intergration question really need help

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ok here is the question:

The curve with equation y=ax^2+bx+c passes through the points P(2,6) and Q(3,16), and has a gradient of 7 at the point P. find the values of the constants a,b, and c.

can anyone plz help me solve this question??? also it will be really appreiciated if all the steps are shown in the calculations. Thanks!!

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when y=6, x=2
6=a(2)^2 + b(2) + c

when y=16, x=3
16=a(3)^2 + b(3) + c

you'll get two equations...subtract them to get an equation with only a and b. Then calculate the derivative of: y=ax^2 + bx + c
you'll get: d(y)/dx = 2ax + b = 7...from this calculate either a or b, when x= 2....
substitute it in any of the above equations and you'll get b (or a) and c

hope that helped... :)

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the fact that the title is "Integration help" is pretty funny given the actual problem :) sorry i had to post on this one, I haven't seen actual calculus questions in a while now >.< by the way, perfect explanation Vasundhra! Exactly how it's supposed to be done.

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