2. The curve with equation y = ax? + 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.

[tex]y = a{x}^{2} + bx + c \\ 6 = a{2}^{2} + 2b + c \\ 6 = 4a+ 2b + c...(1) \\ 16 = 9a+ 3b + c...(2) \\ \frac{dy}{dx} = 7 = 4a + b...(3) \\ (2) - (1) \\ 10= 5a + b...(4) \\ (4) - (3) \\ 5a - 4a = 10 - 7 \\ \boxed{a = 3 }\\ sub \: a \: im \: (4) \\ 10 = 15 + b \\ \boxed{b = - 5} \\ sub \: a \: b \: in \: (1) \\ 6 = 4(3) + 2( - 5) + c \\\boxed{c = 4}[/tex]

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2. The curve with equation y = ax? + 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.​

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2. The curve with equation y = ax? + 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.