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Question Number 166584 by amin96 last updated on 22/Feb/22

Commented by bobhans last updated on 22/Feb/22

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{a}{(\mathrm{x}-2)}^2\Rightarrow 12=\mathrm{a}\left(4\right);\mathrm{a}=3$$$$\mathrm{f}\left(\mathrm{x}\right)=3{(\mathrm{x}-2)}^2\Rightarrow \mathrm{f}\left(10\right)=3\times 64=192$$

Answered by nurtani last updated on 22/Feb/22

$$hightpoint(2,0)\Rightarrow y=f\left(x\right)=a{(x-x_p)}^2+y_p$$$$\Rightarrow y=f\left(x\right)=a{(x-2)}^2+0$$$$\Rightarrow y=f\left(x\right)=a{(x-2)}^2$$$$otherpoint(12,0)$$$$\Rightarrow y=f\left(x\right)=a{(x-2)}^2$$$$12=a{(0-2)}^2$$$$12=a{(-2)}^2$$$$12=4a\Rightarrow a=3$$$$\Rightarrow y=f\left(x\right)=3{(x-2)}^2=3(x^2-4x+4)=3x^2-12x+12$$$$\Rightarrow y=f\left(x\right)=3x^2-12x+12$$$$\therefore x=10\Rightarrow f\left(10\right)=3{\left(10\right)}^2-12\left(10\right)+12$$$$=300-120+12$$$$=192$$$$$$

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