Suppose a, b, c are such that the curve $$y=ax2+bx+c$$ is $$y=3x-3$$ at $$1$$,$$0$$ and is also tangent to $$y=x+1$$ at $$3$$,$$4$$ Then the value of $$2a-b-4c$$ equals $$_____$$

Question

Suppose  a, b, c are such that the curve $$y=ax2+bx+c$$ is $$y=3x-3$$  at  $$1$$,$$0$$ and is also tangent to $$y=x+1$$  at  $$3$$,$$4$$ Then the value of $$2a-b-4c$$ equals $$_____$$

Infinity Learn · Accepted Answer

$$y=ax2+bx+c$$,  $$dydx=2ax+bWhen$$   $$x=1$$,  $$y=0$$∴   $$a+b+c=0$$                                               $$1$$           $$dydxx=1=3$$   and  $$dydxx=3=1$$           $$2a+b=3$$                                              $$2$$            $$6a+b=1$$                                              $$3Solving$$   $$1$$,  $$2$$   and   $$3$$,           $$a=-12$$,  $$b=4$$,   $$c=-72$$∴   $$2a-b-4c=-1-4+14=9$$

Tangents and normals

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Suppose a, b, c are such that the curve $y = {ax}^{2} + bx + c$ is $y = 3 x - 3 at (1, 0)$ and is also tangent to $y = x + 1 at (3, 4)$ Then the value of $(2 a - b - 4 c)$ equals _____

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Tangents and normals

Remember concepts with our Masterclasses.

Suppose a, b, c are such that the curve y=ax2+bx+c is y=3x-3 at 1,0 and is also tangent to y=x+1 at 3,4 Then the value of 2a-b-4c equals _____

y=ax2+bx+c, dydx=2ax+bWhen x=1, y=0∴ a+b+c=0 1 dydxx=1=3 and dydxx=3=1 2a+b=3 2 6a+b=1 3Solving 1, 2 and 3, a=-12, b=4, c=-72∴ 2a-b-4c=-1-4+14=9

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Suppose a, b, c are such that the curve $y = {ax}^{2} + bx + c$ is $y = 3 x - 3 at (1, 0)$ and is also tangent to $y = x + 1 at (3, 4)$ Then the value of $(2 a - b - 4 c)$ equals _____