Solve {l}{0=a(1-h)^2+k}{0=a(-2-h)^2+k}{-2=ah^2+n}

$$\left. \begin{array} { l } { 0 = a ( 1 - h ) ^ { 2 } + k } \\ { 0 = a ( - 2 - h ) ^ { 2 } + k } \\ { - 2 = a h ^ { 2 } + n } \end{array} \right.$$

Solve for a, h, k, n (complex solution)

$$a=0\text{, }h\in \mathrm{C}\text{, }k=0\text{, }n=-2$$

$$a=-\frac{4k}{9}\text{, }h=-\frac{1}{2}=-0.5\text{, }k\in \mathrm{C}\text{, }n=\frac{k-18}{9}$$

Solve for a, h, k, n

$$a=0\text{, }h\in \mathrm{R}\text{, }k=0\text{, }n=-2$$

$$a=-\frac{4k}{9}\text{, }h=-\frac{1}{2}=-0.5\text{, }k\neq 0\text{, }n=\frac{k-18}{9}$$