In vertices of \( \triangle A B C \) lie on \( y=f(x)=a x^{2}+b x+c \). The \( \triangle A B C \...

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In vertices of \( \triangle A B C \) lie on \( y=f(x)=a x^{2}+b x+c \). The \( \triangle A B C \) is right-angled isosceles triangle whose hypotenuse \( A C=4 \sqrt{2} \) units.
\( y=f(x) \) is given by
(a) \( y=x^{2}-2 \sqrt{2} \)
(b) \( y=x^{2}-12 \)
(c) \( y=\frac{x^{2}}{2}-2 \)
(d) \( y=\frac{x^{2}}{2 \sqrt{2}}-2 \sqrt{2} \)
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