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[math SL] Intergration question really need help


hk213

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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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