Question Number 72782 by Mr. K last updated on 02/Nov/19
Commented by Mr. K last updated on 02/Nov/19
$${Find}\:{a},\:{b}\:{and}\:{c} \\ $$
Answered by MJS last updated on 02/Nov/19
$${y}={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${x}=\mathrm{0}\wedge{y}=−\mathrm{4}\:\Rightarrow\:\left(\mathrm{1}\right)\:\:{c}=−\mathrm{4} \\ $$$${x}=\mathrm{2}\wedge{y}=−\mathrm{4}\:\Rightarrow\:\left(\mathrm{2}\right)\:\:\mathrm{4}{a}+\mathrm{2}{b}+{c}=−\mathrm{4} \\ $$$${x}=\mathrm{6}\wedge{y}=\mathrm{8}\:\Rightarrow\:\left(\mathrm{3}\right)\:\:\mathrm{36}{a}+\mathrm{6}{b}+{c}=\mathrm{8} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{4}{a}+\mathrm{2}{b}=\mathrm{0}\:\Rightarrow\:{b}=−\mathrm{2}{a} \\ $$$$\left(\mathrm{3}\right)\:\:\mathrm{36}{a}−\mathrm{12}{a}−\mathrm{4}=\mathrm{8}\:\Rightarrow\:{a}=\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\:{b}=−\mathrm{1} \\ $$$${y}=\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} −{x}−\mathrm{4} \\ $$