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Question Number 56749 by pete last updated on 22/Mar/19

$$\mathrm{The}\mathrm{curve}\mathrm{y}={\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}\mathrm{crosses}\mathrm{the}$$$$\mathrm{y}-\mathrm{axis}\mathrm{at}\mathrm{the}\mathrm{point}(0,3)\mathrm{and}\mathrm{has}$$$$\mathrm{stationary}\mathrm{point}\mathrm{at}(1,2).\mathrm{Find}\mathrm{the}$$$$\mathrm{values}\mathrm{of}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}.$$

Answered by ajfour last updated on 22/Mar/19

$$\mathrm{c}=3$$$$2\mathrm{a}\left(1\right)+\mathrm{b}=0$$$$2=\mathrm{a}+\mathrm{b}+3$$$$\Rightarrow 2\mathrm{a}+2=\mathrm{a}+3\Rightarrow \mathrm{a}=1$$$$\mathrm{and}\mathrm{b}=-2.$$$$\mathrm{y}={\mathrm{x}}^2-2\mathrm{x}+3.$$

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