#### Answer

$a=-\frac{1}{4}$ and so the parabola opens left
$h=23$ and $k=10$ and so the vertex is $(23,10)$. Since the parabola opens left, the axis of symmetry is $y=10$.

#### Work Step by Step

$x=-\frac{1}{4}y^2+5y-2$
$x=-\frac{1}{4}(y^2-20+8)$
$x=-\frac{1}{4}((y-10)^2-100+8)$
$x=-\frac{1}{4}(y-10)^2+23$
$a=-\frac{1}{4}$ and so the parabola opens left
$h=23$ and $k=10$ and so the vertex is $(23,10)$. Since the parabola opens left, the axis of symmetry is $y=10$.