Answer
No graph.
Work Step by Step
\[
0=25-3 x+4 y-8 z+x^{2}+y^{2}+z^{2}
\]
Subtract 25 from each side
\[
-25=-3 x+4 y-8 z+x^{2}+y^{2}+z^{2}
\]
Group like terms
\[
-25=\left(-3 x+x^{2}\right)+\left(-8 z+z^{2}\right)+\left(4 y+y^{2}\right)
\]
Complete the square for each binomial
\[
\frac{9}{4}+4+16-25=\left(4 y+4+y^{2}\right)+\left(-8 z+16+z^{2}\right)+\left(-3 x+\frac{9}{4}+x^{2}\right)
\]
Take each perfect square and simplify the right side
\[
-\frac{11}{4}=(2+y)^{2}+(-4+z)^{2}+\left(-\frac{3}{2}+x\right)^{2}
\]
Equation is in the form
\[
k=\left(-y_{0}+y\right)^{2}+\left(-z_{0}+z\right)^{2}+\left(-x_{0}+x\right)^{2}
\]
With $y_{0}=-2, z_{0}=4, x_{0}=\frac{3}{2}, $ and $k=-\frac{11}{4}$
Since $k<0$, the equation does not satisfy any values of $x, y, z$.
