$\text{a)}$  

$f\left(x\right)=-2{\left(x-1\right)}^2+3$  

$f\left(x\right)=-2\left(x^2-2x+1\right)+3$  

$f\left(x\right)=-2x^2+4x-2+3$  

$f\left(x\right)=-2x^2+4x+1$  

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$\text{b)}$      

$f\left(x\right)=\frac{1}{4}{\left(x+8\right)}^2-12$  

$f\left(x\right)=\frac{1}{4}\left(x^2+16x+64\right)-12$  

$f\left(x\right)=\frac{1}{4}{x}^2+4x+16-12$  

$f\left(x\right)=\frac{1}{4}{x}^2+4x+4$  

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$\text{c)}$  

$f\left(x\right)=3{\left(x-2\right)}^2+5$  

$f\left(x\right)=3\left(x^2-4x+4\right)+5$  

$f\left(x\right)=3x^2-12x+12+5$  

$f\left(x\right)=3x^2-12x+17$