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Question Number 12902 by tawa last updated on 06/May/17

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 06/May/17

1) c=0       (x=0⇒y=0)  y^′ =2ax+b ⇓  2) { ((2a+b=4)),((4a+b=5)) :}⇒2a=1⇒a=(1/2),b=3  y=(1/2)x^2 +3x   . ■

$$\left.\mathrm{1}\right)\:\boldsymbol{{c}}=\mathrm{0}\:\:\:\:\:\:\:\left(\boldsymbol{{x}}=\mathrm{0}\Rightarrow\boldsymbol{{y}}=\mathrm{0}\right) \\ $$$$\boldsymbol{{y}}^{'} =\mathrm{2}\boldsymbol{{ax}}+\boldsymbol{{b}}\:\Downarrow \\ $$$$\left.\mathrm{2}\right)\begin{cases}{\mathrm{2}\boldsymbol{{a}}+\boldsymbol{{b}}=\mathrm{4}}\\{\mathrm{4}\boldsymbol{{a}}+\boldsymbol{{b}}=\mathrm{5}}\end{cases}\Rightarrow\mathrm{2}\boldsymbol{{a}}=\mathrm{1}\Rightarrow\boldsymbol{{a}}=\frac{\mathrm{1}}{\mathrm{2}},\boldsymbol{{b}}=\mathrm{3} \\ $$$$\boldsymbol{{y}}=\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{{x}}\:\:\:.\:\blacksquare \\ $$

Commented by tawa last updated on 06/May/17

God bless you sir.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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